The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes
We construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results are presented to show how our scheme works for preserving discrete extremum principle and positivity on various distorted meshes.
finite volume scheme extremum principle diffusion equation polygonal meshes