Covariance Operator in Reduced Functional

[casanovamaxime]

Hello everyone,
I was wondering if it was possible to add covariance operator in the cost function J we enter in ReducedFunctional(J,m) function
, with m control parameter for optimization problem,
namely instead having the inner product <u,u>_M we have <u,Au>_M where A is an operator we built such as the laplacian one, and M denote the mass matrix,
thanks a lot !

[JHopeCollins]

This is possible by adding additional terms to the cost function. If you have a coefficient nu calculated from your correlation lengthscale and standard deviation then the following should do what you need:

Jhat = assemble(inner(u, u)*dx) + assemble(inner(sqrt(nu)*grad(u), grad(u)*sqrt(nu))*dx)