Integral in DG convection problem

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1

Hi,

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?

Thanks!
Dow

2

Hi Dow,

you can make a system of equations.
Let w be another field variable, and add the equation w’ = u (plus some boundary condition) via a DG method.

You can solve the coupled system via an implicit time-stepping, or play with some combinations of implicit/explicit methods.

Best, Joachim