Hello,
I am writing a DG code for a time-dependent nonlinear PDE and would like to use NGSolve’s built-in Newton solver. Since I understand that the Newton solver does not work directly with a DG formulation, I am introducing a facet variable that is constrained to coincide with the average trace, effectively converting the method into an HDG formulation.
To avoid unnecessary complications, let us consider the standard advection equation with periodic boundary conditions as a test case. The DG method with central fluxes works as expected, but the HDG formulation does not. In 2D, the solution is almost correct, except for some unexpected behavior near the periodic boundaries. In 1D, however, the computed solution is completely wrong.
I have attached the corresponding codes.
Best,
Enrico
TransportHDG2d.ipynb (6.5 KB)
TransportHDG.ipynb (72.1 KB)