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DPG.bib
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@article{Griffiths1997,
abstract = {We use a one-dimensional model problem of advection– diffusion to investigate the treatment recently advocated by Papanastasiou and colleagues to deal with boundary conditions at artificial outflow boundaries. Using finite elements of degree p, we show that their treatment is equivalent to imposing the condition that the (p+1 )st derivative of the dependent variable should vanish at a point close to the outflow. This is then shown to lead to errors of order ðª((h+1/Pe)1.6p+1) in the numerical solutions (where h is the maximum element size and Pe is the global Peclet number), which is superior to the errors of order ðª(hp+1+1/Pe) obtained using a standard no-flux outflow condition. These findings are verified by numerical experiments. {\copyright} 1997 by John Wiley and Sons, Ltd.},
address = {Department of Mathematics and Computer Science, The University, Dundee DD1 4HN, U.K.},
author = {Griffiths, David F.},
citeulike-article-id = {3020995},
citeulike-linkout-0 = {http://dx.doi.org/10.1002/(sici)1097-0363(19970228)24:4%3C393::aid-fld505%3E3.0.co;2-o},
citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/9314/ABSTRACT},
day = {28},
doi = {10.1002/(sici)1097-0363(19970228)24:4%3C393::aid-fld505%3E3.0.co;2-o},
journal = {Int. J. Numer. Meth. Fluids},
month = feb,
number = {4},
pages = {393--411},
posted-at = {2014-01-16 22:27:29},
priority = {2},
publisher = {John Wiley \& Sons, Ltd},
title = {THE 'NO BOUNDARY CONDITION' OUTFLOW BOUNDARY CONDITION},
url = {http://dx.doi.org/10.1002/(sici)1097-0363(19970228)24:4%3C393::aid-fld505%3E3.0.co;2-o},
volume = {24},
year = {1997}
}
@article{Renardy1997,
abstract = {In recent work on outflow boundary conditions for Navier–Stokes equations by Papanastasiou et al. (Int. j. numer. methods fluids, 14, 587–608 (1992)) a choice has been proposed which can formally be described as imposing no boundary condition at all. This of course leads to an underdetermined problem at the level of the partial differential equations. However, it yields a well-defined problem at the discrete level and it has been documented that this choice of outflow conditions performs in a way which is superior to more 'standard' artificial boundary conditions. In this paper we analyse a one-dimensional model problem. We shall show that the 'free' boundary condition of Papanastasiou et al. actually imposes an effective boundary condition. This effective boundary condition is identified and its advantages are discussed. {\copyright} 1997 by John Wiley and Sons, Ltd.},
address = {Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, U.S.A.},
author = {Renardy, Michael},
citeulike-article-id = {4647764},
citeulike-linkout-0 = {http://dx.doi.org/10.1002/(sici)1097-0363(19970228)24:4%3C413::aid-fld507%3E3.0.co;2-n},
citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/9315/ABSTRACT},
day = {28},
doi = {10.1002/(sici)1097-0363(19970228)24:4%3C413::aid-fld507%3E3.0.co;2-n},
journal = {Int. J. Numer. Meth. Fluids},
month = feb,
number = {4},
pages = {413--417},
posted-at = {2014-01-16 22:25:49},
priority = {2},
publisher = {John Wiley \& Sons, Ltd},
title = {IMPOSING 'NO' BOUNDARY CONDITION AT OUTFLOW: WHY DOES IT WORK?},
url = {http://dx.doi.org/10.1002/(sici)1097-0363(19970228)24:4%3C413::aid-fld507%3E3.0.co;2-n},
volume = {24},
year = {1997}
}
@incollection{Carter1973,
author = {Carter, JamesE},
booktitle = {Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics},
citeulike-article-id = {12922010},
citeulike-linkout-0 = {http://dx.doi.org/10.1007/bfb0112678},
citeulike-linkout-1 = {http://link.springer.com/chapter/10.1007/BFb0112678},
doi = {10.1007/bfb0112678},
editor = {Cabannes, Henri and Temam, Roger},
pages = {69--78},
posted-at = {2014-01-15 17:26:00},
priority = {2},
publisher = {Springer Berlin Heidelberg},
series = {Lecture Notes in Physics},
title = {Numerical solutions of the supersonic, laminar flow over a two-dimensional compression corner},
url = {http://dx.doi.org/10.1007/bfb0112678},
volume = {19},
year = {1973}
}
@phdthesis{KirkDissertation,
author = {Kirk, Benjamin},
citeulike-article-id = {12921981},
institution = {Computational and Applied Mathematics},
posted-at = {2014-01-15 16:52:18},
priority = {2},
school = {University of Texas at Austin},
title = {Adaptive Finite Element Simulation of Flow and Transport Applications on Parallel Computers},
year = {2009}
}
@article{Burgers2D,
abstract = {In this paper, the discrete Adomian decomposition method (ADM) is proposed to numerically solve the two-dimensional Burgers' nonlinear difference equations. Two test problems are considered to illustrate the accuracy of the proposed discrete decomposition method. It is shown that the numerical results are in good agreement with the exact solutions for each problem.},
author = {Zhu, Hongqing and Shu, Huazhong and Ding, Meiyu},
citeulike-article-id = {7397155},
citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.camwa.2010.05.031},
day = {15},
doi = {10.1016/j.camwa.2010.05.031},
issn = {08981221},
journal = {Computers \& Mathematics with Applications},
month = aug,
number = {3},
pages = {840--848},
posted-at = {2014-01-02 22:20:49},
priority = {2},
title = {Numerical solutions of two-dimensional Burgers' equations by discrete Adomian decomposition method},
url = {http://dx.doi.org/10.1016/j.camwa.2010.05.031},
volume = {60},
year = {2010}
}
@article{Bijl2002,
author = {Bijl, Hester and Carpenter, Mark H. and Vatsa, Veer N. and Kennedy, Christopher A.},
citeulike-article-id = {10785709},
citeulike-linkout-0 = {http://dx.doi.org/10.1006/jcph.2002.7059},
doi = {10.1006/jcph.2002.7059},
issn = {00219991},
journal = {Journal of Computational Physics},
month = jun,
number = {1},
pages = {313--329},
posted-at = {2014-01-02 18:02:10},
priority = {0},
title = {Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow},
url = {http://dx.doi.org/10.1006/jcph.2002.7059},
volume = {179},
year = {2002}
}
@techreport{Ellis2013Report,
author = {Ellis, Truman E. and Demkowicz, Leszek F. and Chan, Jesse L.},
citeulike-article-id = {12859367},
institution = {ICES},
month = dec,
posted-at = {2013-12-23 20:58:51},
priority = {2},
title = {Locally Conservative Discontinuous Petrov-Galerkin Finite Elements For Fluid Problems},
year = {2013}
}
@phdthesis{NateDissertation,
author = {Roberts, Nathan V.},
citeulike-article-id = {12857052},
posted-at = {2013-12-19 22:58:59},
priority = {2},
school = {University of Texas at Austin},
title = {A Discontinuous {P}etrov-{G}alerkin Methodology for Incompressible Flow Problems},
year = {2013}
}
@phdthesis{JesseDissertation,
author = {Chan, Jesse L.},
citeulike-article-id = {12857049},
posted-at = {2013-12-19 22:56:55},
priority = {2},
school = {University of Texas at Austin},
title = {A {DPG} Method for Convection-Diffusion Problems},
year = {2013}
}
@article{Klaij2006,
abstract = {A space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations is presented. We explain the space-time setting, derive the weak formulation and discuss our choices for the numerical fluxes. The resulting numerical method allows local grid adaptation as well as moving and deforming boundaries, which we illustrate by computing the flow around a 3D delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2D airfoil in rapid pitch-up maneuver.},
address = {San Diego, CA, USA},
author = {Klaij, C. M. and van der Vegt, J. J. W. and van der Ven, H.},
citeulike-article-id = {12851481},
citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1217520.1217535},
citeulike-linkout-1 = {http://dx.doi.org/10.1016/j.jcp.2006.01.018},
doi = {10.1016/j.jcp.2006.01.018},
issn = {0021-9991},
journal = {J. Comput. Phys.},
month = sep,
number = {2},
pages = {589--611},
posted-at = {2013-12-17 21:57:06},
priority = {2},
publisher = {Academic Press Professional, Inc.},
title = {Space-time Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations},
url = {http://dx.doi.org/10.1016/j.jcp.2006.01.018},
volume = {217},
year = {2006}
}
@article{Rhebergen2013,
abstract = {We introduce a space-time discontinuous Galerkin (DG) finite element method for the incompressible Navier-Stokes equations. Our formulation can be made arbitrarily high-order accurate in both space and time and can be directly applied to deforming domains. Different stabilizing approaches are discussed which ensure stability of the method. A numerical study is performed to compare the effect of the stabilizing approaches, to show the method's robustness on deforming domains and to investigate the behavior of the convergence rates of the solution. Recently we introduced a space-time hybridizable DG (HDG) method for incompressible flows [S. Rhebergen, B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, J. Comput. Phys. 231 (2012) 4185-4204]. We will compare numerical results of the space-time DG and space-time HDG methods. This constitutes the first comparison between DG and HDG methods.},
address = {San Diego, CA, USA},
author = {Rhebergen, Sander and Cockburn, Bernardo and Van Der Vegt, Jaap J. W.},
citeulike-article-id = {11291615},
citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=2397727.2397978},
citeulike-linkout-1 = {http://dx.doi.org/10.1016/j.jcp.2012.08.052},
doi = {10.1016/j.jcp.2012.08.052},
issn = {0021-9991},
journal = {J. Comput. Phys.},
month = jan,
pages = {339--358},
posted-at = {2013-12-17 21:54:28},
priority = {2},
publisher = {Academic Press Professional, Inc.},
title = {A Space-time Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations},
url = {http://dx.doi.org/10.1016/j.jcp.2012.08.052},
volume = {233},
year = {2013}
}
@article{CostabelMcIntosh,
abstract = {We study integral operators related to a regularized version of the classical Poincar\'{e} path integral and the adjoint class generalizing Bogovski\u{i}'s integral operator, acting on differential forms in
\${\mathbb{R}^n}\$
. We prove that these operators are pseudodifferential operators of order −1. The Poincar\'{e}-type operators map polynomials to polynomials and can have applications in finite element analysis. For a domain starlike with respect to a ball, the special support properties of the operators imply regularity for the de Rham complex without boundary conditions (using Poincar\'{e}-type operators) and with full Dirichlet boundary conditions (using Bogovski\u{i}-type operators). For bounded Lipschitz domains, the same regularity results hold, and in addition we show that the cohomology spaces can always be represented by
\${\fancyscript{C}^{\infty}}\$
functions.},
author = {Costabel, Martin and McIntosh, Alan},
booktitle = {Mathematische Zeitschrift},
citeulike-article-id = {4495628},
citeulike-linkout-0 = {http://dx.doi.org/10.1007/s00209-009-0517-8},
citeulike-linkout-1 = {http://www.springerlink.com/content/q6146wlnl2145x82},
citeulike-linkout-2 = {http://link.springer.com/article/10.1007/s00209-009-0517-8},
doi = {10.1007/s00209-009-0517-8},
journal = {Mathematische Zeitschrift},
number = {2},
pages = {297--320},
posted-at = {2013-12-17 20:02:04},
priority = {2},
publisher = {Springer-Verlag},
title = {On {B}ogovski\u{i} and regularized {P}oincar\'{e} integral operators for de {R}ham complexes on {L}ipschitz domains},
url = {http://dx.doi.org/10.1007/s00209-009-0517-8},
volume = {265},
year = {2010}
}
@inproceedings{Lew2003,
abstract = {We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime form of a discrete version of Hamilton\^{a}s variational principle. As a consequence of this variational structure, the algorithms conserve local momenta and a local discrete multisymplectic structure exactly. To guide the development of the discretizations, a spacetime multisymplectic formulation of elastodynamics is presented. The variational principle used incorporates both configuration and spacetime reference variations. This allows a unified treatment of all the conservation properties of the system. A discrete version of reference configuration is also considered, providing a natural definition of a discrete energy. The possibilities for discrete energy conservation are evaluated. Numerical tests reveal that, even when local energy balance is not enforced exactly, the global and local energy behavior of the AVIs is quite remarkable, a property which can probably be traced to the symplectic nature of the algorithm.},
author = {Lew, A. and Marsden, J. E. and Ortiz, M. and West, M.},
booktitle = {ARCH. RATIONAL MECH. ANAL.},
citeulike-article-id = {12851064},
citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.6730},
keywords = {avi},
posted-at = {2013-12-17 20:00:37},
priority = {0},
title = {Asynchronous Variational Integrators},
url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.6730},
year = {2003}
}
@techreport{DBB05,
author = {Demkowicz, L.},
citeulike-article-id = {12794408},
institution = {ICES},
keywords = {dpg},
posted-at = {2013-11-19 19:39:20},
priority = {2},
title = {Babu\v{s}ka $\Leftrightarrow$ {B}rezzi?},
year = {2006}
}
@book{fenics:book,
citeulike-article-id = {12794407},
citeulike-linkout-0 = {http://dx.doi.org/10.1007/978-3-642-23099-8},
doi = {10.1007/978-3-642-23099-8},
editor = {Logg, A. and Mardal, K. A. and Wells, G. N.},
keywords = {dpg},
posted-at = {2013-11-19 19:39:20},
priority = {2},
publisher = {Springer},
series = {Lecture Notes in Computational Science and Engineering},
title = {Automated Solution of Differential Equations by the Finite Element Method},
url = {http://dx.doi.org/10.1007/978-3-642-23099-8},
volume = {84},
year = {2012}
}
@article{DPG4,
author = {Zitelli, J. and Muga, I. and Demkowicz, L. and Gopalakrishnan, J. and Pardo, D. and Calo, V.},
citeulike-article-id = {12794406},
journal = {J. Comp. Phys.},
keywords = {dpg},
pages = {2406--2432},
posted-at = {2013-11-19 19:39:20},
priority = {2},
title = {A Class of Discontinuous {P}etrov-{G}alerkin Methods. {Part IV:} {W}ave Propagation Problems},
volume = {230},
year = {2011}
}
@article{ZhuSchotzau10,
author = {Zhu, I. and Sch\"{o}tzau},
citeulike-article-id = {12794405},
journal = {IMA Journal of Numerical Analysis},
keywords = {dpg},
note = {Advance Access published April 28, 2010},
pages = {1--35},
posted-at = {2013-11-19 19:39:20},
priority = {2},
title = {A Robust a Posteriori Error Estimate for $hp$-Adaptive DG methods for Convection-Diffusion Equations},
year = {2010}
}
@article{FengWu09,
author = {Feng and Wu},
citeulike-article-id = {12794404},
journal = {SIAM J. Numer. Anal.},
keywords = {dpg},
number = {4},
pages = {2872--2896},
posted-at = {2013-11-19 19:39:20},
priority = {2},
title = {Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number},
volume = {47},
year = {2009}
}
@article{Williamson1996,
author = {Williamson, C. H. K.},
citeulike-article-id = {12794403},
journal = {Annual review of Fluid Mechanics},
keywords = {dpg, immersed\_boundaries, wall-modeling},
pages = {477--539},
posted-at = {2013-11-19 19:39:20},
priority = {0},
title = {{Vortex dynamics in the cylinder wake}},
volume = {28},
year = {1996}
}
@book{IntroCFD,
author = {Versteeg, H. K. and Malalasekera, W.},
citeulike-article-id = {12794402},
citeulike-linkout-0 = {http://books.google.com/books?id=RvBZ-UMpGzIC},
keywords = {dpg},
posted-at = {2013-11-19 19:39:20},
priority = {2},
publisher = {Prentice Hall},
title = {An Introduction to Computational Fluid Dynamics: The Finite Volume Method},
url = {http://books.google.com/books?id=RvBZ-UMpGzIC},
year = {2007}
}
@article{Temam69.II,
author = {Temam, Roger},
citeulike-article-id = {12794401},
journal = {Arch. Rational Mech. Anal.},
keywords = {dpg},
pages = {377--385},
posted-at = {2013-11-19 19:39:20},
priority = {2},
title = {Sur l'approximation de la solution des \'{e}quations de {N}avier-{S}tokes par la m\'{e}thode des pas fractionnaires ({II})},
volume = {33},
year = {1969}
}
@article{Temam69.I,
author = {Temam, Roger},
citeulike-article-id = {12794400},
journal = {Arch. Rational Mech. Anal.},
keywords = {dpg},
pages = {135--153},
posted-at = {2013-11-19 19:39:20},
priority = {2},
title = {Sur l'approximation de la solution des \'{e}quations de {N}avier-{S}tokes par la m\'{e}thode des pas fractionnaires ({I})},
volume = {32},
year = {1969}
}
@phdthesis{Strikwerda76,
author = {Strikwerda, J. C.},
citeulike-article-id = {12794399},
keywords = {dpg},
posted-at = {2013-11-19 19:39:20},
priority = {2},
school = {Dept. of Math., Standford},
title = {Initial Boundary Value Problems for Incompletely Parabolic Problems},
year = {1976}
}
@book{Showalter,
address = {London},
author = {Showalter, R. E.},
citeulike-article-id = {12794398},
keywords = {dpg},
posted-at = {2013-11-19 19:39:19},
priority = {2},
publisher = {Pitman Publishing Limited},
title = {Hilbert Space Methods for Partial Differential Equations},
year = {1977}
}
@incollection{shewchuk96b,
author = {Shewchuk, Jonathan R.},
booktitle = {Applied Computational Geometry: Towards Geometric Engineering},
citeulike-article-id = {12794397},
editor = {Lin, Ming C. and Manocha, Dinesh},
keywords = {dpg},
month = may,
note = {From the First ACM Workshop on Applied Computational Geometry},
pages = {203--222},
posted-at = {2013-11-19 19:39:19},
priority = {2},
publisher = {Springer-Verlag},
series = {Lecture Notes in Computer Science},
title = {Triangle: {E}ngineering a {2D} {Q}uality {M}esh {G}enerator and {D}elaunay {T}riangulator},
volume = {1148},
year = {1996}
}
@article{SchwabSuri96,
author = {Schwab, C. and Suri, M.},
citeulike-article-id = {12794396},
journal = {Math. Comput.},
keywords = {dpg},
number = {216},
pages = {1403--1429},
posted-at = {2013-11-19 19:39:19},
priority = {2},
title = {The $p$ and $hp$ versions of the finite element method for problems with boundary layers},
volume = {65},
year = {1996}
}
@book{RoosStynesTobiska08,
address = {Berlin},
author = {Roos, H. G. and Stynes, M. and Tobiska, L.},
citeulike-article-id = {12794395},
edition = {2nd},
keywords = {dpg},
posted-at = {2013-11-19 19:39:19},
priority = {2},
publisher = {Springer-Verlag},
series = {Springer Series in Computational Mathematics},
title = {Robust Numerical Methods for Singularly Perturbed Differential Equations},
volume = {24},
year = {2008}
}
@book{roos2008robust,
author = {Roos, H. and Stynes, M. and Tobiska, L.},
citeulike-article-id = {12794394},
citeulike-linkout-0 = {http://books.google.com/books?id=tdnw1p2JoEIC},
keywords = {dpg},
posted-at = {2013-11-19 19:39:19},
priority = {2},
publisher = {Springer},
series = {Springer series in computational mathematics},
title = {Robust numerical methods for singularly perturbed differential equations: convection-diffusion-reaction and flow problems},
url = {http://books.google.com/books?id=tdnw1p2JoEIC},
year = {2008}
}
@techreport{Roberts2011,
author = {Roberts, Nathan V. and Ridzal, Denis and Bochev, Pavel B. and Demkowicz, Leszek F.},
citeulike-article-id = {12794393},
citeulike-linkout-0 = {https://cfwebprod.sandia.gov/cfdocs/CCIM/docs/Roberts_et_al_SAND2011-6678.pdf},
institution = {Sandia National Laboratories},
keywords = {dpg},
number = {SAND2011-6678},
posted-at = {2013-11-19 19:39:19},
priority = {2},
title = {{A Toolbox for a Class of Discontinuous Petrov-Galerkin Methods Using Trilinos}},
url = {https://cfwebprod.sandia.gov/cfdocs/CCIM/docs/Roberts_et_al_SAND2011-6678.pdf},
year = {2011}
}
@techreport{DPGStokes,
annote = {Submitted to Computers \& Mathematics with Applications.},
author = {Roberts, Nathan V. and Bui-Thanh, Tan and Demkowicz, Leszek F.},
citeulike-article-id = {12794392},
citeulike-linkout-0 = {http://www.ices.utexas.edu/media/reports/2012/1222.pdf},
institution = {ICES},
keywords = {dpg},
number = {12-22},
posted-at = {2013-11-19 19:39:19},
priority = {2},
title = {The {DPG} Method for the {S}tokes Problem},
url = {http://www.ices.utexas.edu/media/reports/2012/1222.pdf},
year = {2012}
}
@incollection{Roberts2010,
author = {Roberts, N. V. and Ridzal, D. and Bochev, P. N. and Demkowicz, L. and Peterson, K. J. and Siefert, C. M.},
booktitle = {CSRI Summer Proceedings 2010},
citeulike-article-id = {12794391},
keywords = {dpg},
posted-at = {2013-11-19 19:39:19},
priority = {2},
publisher = {Sandia National Laboratories},
title = {Application of a Discontinuous {P}etrov-{G}alerkin Method to the {S}tokes Equations},
year = {2010}
}
@electronic{Rannacher99,
author = {Rannacher, Rolf},
citeulike-article-id = {12794390},
citeulike-linkout-0 = {http://www.numerik.uni-hd.de/Oberwolfach-Seminar/CFD-Course.pdf},
keywords = {dpg},
posted-at = {2013-11-19 19:39:19},
priority = {2},
title = {Finite Element Methods for the Incompressible {N}avier-{S}tokes Equations (lecture notes)},
url = {http://www.numerik.uni-hd.de/Oberwolfach-Seminar/CFD-Course.pdf},
year = {1999}
}
@article{Perot2011,
author = {Perot, J. B.},
citeulike-article-id = {12794389},
citeulike-linkout-0 = {http://dx.doi.org/10.1146/annurev-fluid-122109-160645},
doi = {10.1146/annurev-fluid-122109-160645},
institution = {University of Massachusetts, Amherst},
journal = {Annual Review of Fluid Mechanics},
keywords = {dpg},
pages = {299--318},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {Discrete Conservation Properties of Unstructured Mesh Schemes},
url = {http://dx.doi.org/10.1146/annurev-fluid-122109-160645},
volume = {43},
year = {2011}
}
@article{OrszagEtAl,
author = {Orszag, Steven A. and Israeli, Moshe and Deville, Michel O.},
citeulike-article-id = {12794388},
citeulike-linkout-0 = {http://www.springerlink.com/index/10.1007/BF01061454},
journal = {Journal of Scientific Computing},
keywords = {dpg},
number = {1},
pages = {75--111},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Springer},
title = {Boundary conditions for incompressible flows},
url = {http://www.springerlink.com/index/10.1007/BF01061454},
volume = {1},
year = {1986}
}
@book{OdenDemkowicz10,
author = {Oden, J. Tinsley and Demkowicz, Leszek F.},
citeulike-article-id = {12794387},
keywords = {dpg},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {CRC Press},
title = {Applied functional analysis},
year = {2010}
}
@book{FAbook,
address = {Boca Raton},
author = {Oden, J. T. and Demkowicz, L. F.},
citeulike-article-id = {12794386},
keywords = {dpg},
note = {Second edition},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Chapman \& Hall/CRC Press},
title = {Applied Functional Analysis for Science and Engineering},
year = {2010}
}
@article{NiemiBramwellDemkowicz10,
author = {Niemi, A. H. and Bramwell, J. A. and Demkowicz, L. F.},
citeulike-article-id = {12794385},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {dpg},
month = feb,
number = {9-12},
pages = {1291--1300},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {{Discontinuous Petrov--Galerkin} Method with Optimal Test Functions for Thin-Body Problems in Solid Mechanics},
volume = {200},
year = {2011}
}
@article{NguyenPeraireCockburn09,
author = {Nguyen, N. and Peraire, J. and Cockburn, B.},
citeulike-article-id = {12794384},
journal = {Journal of Computational Physics},
keywords = {dpg},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {An Implicit High-order Hybridizable Discontinuous {G}alerkin Method for Linear Convection--Diffusion Equations},
volume = {228},
year = {2009}
}
@article{N80,
author = {N\'{e}d\'{e}lec, J. C.},
citeulike-article-id = {12794383},
journal = {Numer. Math.},
keywords = {dpg},
pages = {315--341},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {Mixed Finite Elements in \${\\doubleIR}^3\$},
volume = {35},
year = {1980}
}
@article{MoroNguyenPeraire11,
author = {Moro, D. and Nguyen, N. C. and Peraire, J.},
citeulike-article-id = {12794382},
journal = {Int.J. Num. Meth. Eng.},
keywords = {dpg},
note = {in print},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {A Hybridized Discontinuous {P}etrov-{G}alerkin Scheme for Scalar Conservation Laws},
year = {2011}
}
@article{Moffat,
author = {Moffat, H. K.},
citeulike-article-id = {12794381},
journal = {Journal of Fluid Mechanics},
keywords = {dpg},
number = {1},
pages = {1--18},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {Viscous and Resistive Eddies Near a Sharp Corner},
volume = {18},
year = {1964}
}
@article{REFTREE,
author = {Mitchell, W. F.},
citeulike-article-id = {12794380},
journal = {Journal of Parallel and Distributed Computing},
keywords = {dpg},
pages = {417--429},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {A Refinement-tree Based Partitioning Method for Dynamic Load Balancing with Adaptively Refined Grids},
volume = {67},
year = {2007}
}
@book{Melenk02,
address = {Berlin},
author = {Melenk, J. M.},
citeulike-article-id = {12794379},
keywords = {dpg},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Springer},
title = {$hp$-{Finite Element Methods for Singular Perturbations}},
year = {2002}
}
@book{McLean,
author = {McLean, W.},
citeulike-article-id = {12794378},
keywords = {dpg},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Cambridge University Press},
title = {Strongly Elliptic Systems and Boundary Integral Equations},
year = {2000}
}
@book{Ladyzhenskaya,
author = {Ladyzhenskaya, O. A.},
citeulike-article-id = {12794377},
keywords = {dpg},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Gordon and Breach, London},
title = {The Mathematical Theory of Viscous Incompressible Flows},
year = {1969}
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@article{Kovasznay,
author = {Kovasznay, L. I. G.},
citeulike-article-id = {12794376},
citeulike-linkout-0 = {http://dx.doi.org/10.1017/S0305004100023999},
doi = {10.1017/S0305004100023999},
eprint = {http://journals.cambridge.org/article\_S0305004100023999},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
keywords = {dpg},
number = {01},
pages = {58--62},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {Laminar flow behind a two-dimensional grid},
url = {http://dx.doi.org/10.1017/S0305004100023999},
volume = {44},
year = {1948}
}
@article{KovasznayCylinder,
author = {Kovasznay, L. S. G.},
citeulike-article-id = {12794375},
journal = {Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences},
keywords = {dpg},
number = {1053},
pages = {174--190},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {Hot-Wire Investigation of the Wake behind Cylinders at Low {R}eynolds Numbers},
volume = {198},
year = {1949}
}
@article{Kirk2006,
address = {London, UK, UK},
author = {Kirk, Benjamin S. and Peterson, John W. and Stogner, Roy H. and Carey, Graham F.},
citeulike-article-id = {12794374},
citeulike-linkout-0 = {http://dx.doi.org/10.1007/s00366-006-0049-3},
doi = {10.1007/s00366-006-0049-3},
journal = {Eng. with Comput.},
keywords = {adaptive, computing, dpg, elements, finite, mesh, parallel, refinement},
month = dec,
number = {3},
pages = {237--254},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Springer-Verlag},
title = {lib{M}esh: a {C}++ library for parallel adaptive mesh refinement/coarsening simulations},
url = {http://dx.doi.org/10.1007/s00366-006-0049-3},
volume = {22},
year = {2006}
}
@article{KarniadakisEtAl,
author = {Karniadakis, G. and Israeli, M. and Orszag, S.},
citeulike-article-id = {12794373},
citeulike-linkout-0 = {http://linkinghub.elsevier.com/retrieve/pii/0021999191900078},
journal = {Journal of Computational Physics},
keywords = {dpg},
number = {2},
pages = {414--443},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Elsevier},
title = {High-order splitting methods for the incompressible Navier-Stokes equations},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999191900078},
volume = {97},
year = {1991}
}
@book{Ihlenburg,
address = {New York},
author = {Ihlenburg, F.},
citeulike-article-id = {12794372},
keywords = {dpg},
posted-at = {2013-11-19 19:39:18},
priority = {2},
publisher = {Springer-Verlag},
series = {Applied Mathematical Sciences},
title = {Finite Element Analysis of Acoustic Scattering},
volume = {132},
year = {1998}
}
@article{HuttunenMonkKaipio02,
author = {Huttunen, T. and Monk and Kaipio, J. P.},
citeulike-article-id = {12794371},
journal = {J. Comp. Phys.},
keywords = {dpg},
number = {1},
pages = {27--46},
posted-at = {2013-11-19 19:39:18},
priority = {2},
title = {Computational Aspects of the Ultra-Weak Variational Formulation},
volume = {182},
year = {2002}
}
@article{Hughes,
author = {Hughes, Thomas J. R. and Scovazzi, Guglielmo and Bochev, Pavel B. and Buffa, Annalisa},
citeulike-article-id = {12794370},
citeulike-linkout-0 = {http://dx.doi.org/DOI:%2010.1016/j.cma.2005.06.006},
citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6V29-4HMFJ5F-1/2/5541b393360c41d7bbcbcfe9b9e252bd},
doi = {DOI:%2010.1016/j.cma.2005.06.006},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {dpg, galerkin, methods},
number = {19-22},
pages = {2761--2787},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {{A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method}},
url = {http://www.sciencedirect.com/science/article/B6V29-4HMFJ5F-1/2/5541b393360c41d7bbcbcfe9b9e252bd},
volume = {195},
year = {2006}
}
@article{HughesFrancaMallet86,
author = {Hughes, T. J. R. and Franca, L. P. and Mallet, M.},
citeulike-article-id = {12794369},
journal = {Comput. Methods Appl. Mech. Engrg.},
keywords = {dpg},
pages = {223--234},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {A New Finite Element Formulation for Computational Fluid Dynamics: I. {S}ymmetric Forms of the Compressible {E}uler and {N}avier-{S}tokes Equations and the Second Law of Thermodynamics},
volume = {54},
year = {1986}
}
@article{HoustonSchwabSuli00,
author = {Houston, P. and Schwab, C. and {} and S{\"{u}}li, E.},
citeulike-article-id = {12794368},
journal = {SIAM J. Numer. Anal.},
keywords = {dpg},
note = {(electronic)},
pages = {1618--1643},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {Stabilized $hp$-Finite Element Methods for First-order Hyperbolic Problems},
volume = {37},
year = {2000}
}
@article{HoustonSchwabSuli02,
author = {Houston, P. and Schwab, C. and {} and S{\"{u}}li, E.},
citeulike-article-id = {12794367},
journal = {SIAM J. Numer. Anal.},
keywords = {dpg},
pages = {2133--2163},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {Discontinuous $hp$-Finite Element Methods for Advection-Diffusion-Reaction Problems},
volume = {39},
year = {2002}
}
@article{Trilinos,
address = {New York, NY, USA},
author = {Heroux, Michael A. and Bartlett, Roscoe A. and Howle, Vicki E. and Hoekstra, Robert J. and Hu, Jonathan J. and Kolda, Tamara G. and Lehoucq, Richard B. and Long, Kevin R. and Pawlowski, Roger P. and Phipps, Eric T. and Salinger, Andrew G. and Thornquist, Heidi K. and Tuminaro, Ray S. and Willenbring, James M. and Williams, Alan and Stanley, Kendall S.},
citeulike-article-id = {12794366},
citeulike-linkout-0 = {http://dx.doi.org/http://doi.acm.org/10.1145/1089014.1089021},
doi = {http://doi.acm.org/10.1145/1089014.1089021},
journal = {ACM Trans. Math. Softw.},
keywords = {dpg},
number = {3},
pages = {397--423},
posted-at = {2013-11-19 19:39:17},
priority = {2},
publisher = {ACM Press},
title = {{An overview of the Trilinos project}},
url = {http://dx.doi.org/http://doi.acm.org/10.1145/1089014.1089021},
volume = {31},
year = {2005}
}
@article{GuermondShen,
author = {Guermond, J. L. and Shen, Jie},
citeulike-article-id = {12794365},
journal = {J. Comput. Phys.},
keywords = {dpg},
pages = {262--276},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {A new class of truly consistent splitting schemes for incompressible flows},
volume = {192},
year = {2003}
}
@article{Guermond06,
author = {Guermond, J. L. and Minev, P. and Shen, Jie},
citeulike-article-id = {12794364},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {dpg},
pages = {6011--6045},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {An overview of projection methods for incompressible flows},
volume = {195},
year = {2006}
}
@article{GuermondMinev2011,
author = {Guermond, J. L. and Minev, P. D.},
citeulike-article-id = {12794363},
citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.cma.2011.02.007},
citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/pii/S0045782511000429},
doi = {10.1016/j.cma.2011.02.007},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {dpg, splitting, time},
number = {23--24},
pages = {2083--2093},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {A new class of massively parallel direction splitting for the incompressible {N}avier--{S}tokes equations},
url = {http://www.sciencedirect.com/science/article/pii/S0045782511000429},
volume = {200},
year = {2011}
}
@article{FLD:FLD505,
author = {Griffiths, D.},
citeulike-article-id = {12794362},
citeulike-linkout-0 = {http://dx.doi.org/10.1002/(SICI)1097-0363(19970228)24:4%3C393::AID-FLD505%3E3.0.CO;2-O},
doi = {10.1002/(SICI)1097-0363(19970228)24:4%3C393::AID-FLD505%3E3.0.CO;2-O},
journal = {International Journal for Numerical Methods in Fluids},
keywords = {advection, boundary, conditions, diffusion, dpg, elements, finite, outflow},
number = {4},
pages = {393--411},
posted-at = {2013-11-19 19:39:17},
priority = {2},
publisher = {John Wiley \& Sons, Ltd},
title = {The `no boundary condition' outflow boundary condition},
url = {http://dx.doi.org/10.1002/(SICI)1097-0363(19970228)24:4%3C393::AID-FLD505%3E3.0.CO;2-O},
volume = {24},
year = {1997}
}
@techreport{practicalDPG,
author = {Gopalakrishnan, J. and Qiu, W.},
citeulike-article-id = {12794361},
institution = {IMA},
keywords = {dpg},
note = {submitted},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {An analysis of the practical {DPG} method},
year = {2011}
}
@article{GopalakrishnanQiu11,
author = {Gopalakrishnan, Jay and Qiu, Weifeng},
citeulike-article-id = {12794360},
journal = {Mathematics of Computation},
keywords = {dpg, practical, proof},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {{An analysis of the practical DPG method}},
year = {2012}
}
@article{Givoli88,
author = {Givoli, D.},
citeulike-article-id = {12794359},
journal = {Internat.J.Numer.Methods Engrg.},
keywords = {dpg},
number = {6},
pages = {1281--1298},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {Nonlocal and Semilocal Optimal Weighting Functions for Symmetric Problems Involving a Small Parameter},
volume = {26},
year = {1988}
}
@book{Gilbarg,
author = {Gilbarg, D. and Trudinger, N. S.},
citeulike-article-id = {12794358},
keywords = {dpg},
posted-at = {2013-11-19 19:39:17},
priority = {2},
publisher = {Springer-Verlag},
title = {Elliptic Partial Differential Equations of Second Order},
year = {1983}
}
@article{FLD:FLD582,
author = {Gerbeau, J. F. and Bris, C. Le and Bercovier, M.},
citeulike-article-id = {12794357},
journal = {International Journal for Numerical Methods in Fluids},
keywords = {body, dpg, flow, force, incompressible, method, projection},
number = {6},
pages = {679--695},
posted-at = {2013-11-19 19:39:17},
priority = {2},
publisher = {John Wiley \& Sons, Ltd},
title = {Spurious velocities in the steady flow of an incompressible fluid subjected to external forces},
volume = {25},
year = {1997}
}
@book{GoFBook,
address = {Boston, MA, USA},
author = {Gamma, Erich and Helm, Richard and Johnson, Ralph and Vlissides, John},
citeulike-article-id = {12794356},
keywords = {dpg},
posted-at = {2013-11-19 19:39:17},
priority = {2},
publisher = {Addison-Wesley Longman Publishing Co., Inc.},
title = {Design patterns: elements of reusable object-oriented software},
year = {1995}
}
@article{Friedrichs58,
author = {Friedrichs, Kurt O.},
citeulike-article-id = {12794355},
journal = {Communications on pure and applied mathematics},
keywords = {dpg},
pages = {333--418},
posted-at = {2013-11-19 19:39:17},
priority = {2},
title = {Symmetric positive linear differential Equations},
volume = {XI},
year = {1958}
}
@book{Folland,
author = {Folland, G. B.},
citeulike-article-id = {12794354},
keywords = {dpg},
posted-at = {2013-11-19 19:39:17},
priority = {2},
publisher = {Princeton},
title = {Introduction to Partial Differential Equations},
year = {1976}
}
@book{FFS03,
address = {Oxford},
author = {Feistauer, M. and Felcman, J. and Straskraba, I.},
citeulike-article-id = {12794353},
keywords = {dpg},
note = {ISBN 0-19-850588-4},
posted-at = {2013-11-19 19:39:17},
priority = {2},
publisher = {Clarendon Press},
title = {Mathematical and Computational Methods for Compressible Flow},
year = {2003}