Custom Bilinear Form

[m-reichelt]

Hello!
Hopefully I do not ask anything that is answered somewhere in the documentation.
Specifically I want to implement

where Y is a fixed value for all testfunctions.
So for most testfunctions it is just the regular stiffness matrix with a minus, but for some it is different.
I looked into nonlinear forms, but I do not think that this is the right way.

Thank you in advance for your help.
Greetings Michael

[vladotomov]

One approach is to create a new integrator by taking the code from the existing DiffusionIntegrator and write some custom logic around the el.CalcDShape(ip, dshape);, by playing with the quadrature point y-position.

[m-reichelt]

Thank you. I will keep that in mind. I am now trying a different approach for better testability (I directly construct the operator which modifies v(x.y) -> v(x,Y)-v(x,y) and construct its matrix by bilinear form in H1 space. Then I realize the bilinear form with the constructed matrices.
I will keep you updated, if I try out your approach.