We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
12/2007
Error estimates for a mixed finite element discretization of some degenerate parabolic equations
Florin Adrian Radu, Iuliu Sorin Pop and Peter Knabner
Abstract
We consider a numerical scheme for a class of degenerate parabolic equations, including both slow and fast diffusion cases. A particular example in this sense is the Richards' equation modeling the flow in porous media. The numerical scheme is based on the mixed finite element method (MFEM) in space, and is of first order implicit in time. The lowest order Raviart-Thomas elements are used. We derive error estimates in terms of the discretization parameters and show the convergence of the scheme. The paper is concluded by numerical examples.
