Error estimates for the finite volume discretization for the porous medium equation

摘要

We analyze the convergence of a numerical scheme for a class of degenerate parabolic problems modelling reactions in porous media, and involving a nonlinear, possibly vanishing diffusion. The scheme involves the Kirchhoff transformation of the regularized nonlinearity, as well as an Euler implicit time stepping and triangle based finite volumes. We prove the convergence of the approach by giving error estimates in terms of the discretization and regularization parameter.