I’m trying to solve a DG convection problem with a nonlinear convection term that includes the integral of the function I’m solving for. The problem is essentially something like this:
Solve for u: du/dt - (cuu*w)’ = 0, where w is the integral of u (i.e. u = w’) and c is a constant
I was thinking I might be able to create a custom CoefficientFunction for w, which would integrate the function u over the mesh at each time step and store values so they could be returned by calls to Evaluate().
I have a feeling there is a more clever way to accomplish this sort of thing in Ngsolve. Any suggestions?