Anisotropic Mesh Adaptation for Finite Element Solution of Anisotropic Porous Medium Equation

TL;DR

This paper introduces anisotropic mesh adaptation techniques for solving the anisotropic porous medium equation, demonstrating second order convergence in numerical solutions for 2D cases.

Contribution

It extends the porous medium equation to anisotropic media and develops anisotropic mesh adaptation methods for finite element solutions, including analytical solutions and numerical validation.

Findings

Second order convergence achieved with anisotropic adaptive meshes

Analytical solution derived for time-independent APME

Numerical results confirm effectiveness of anisotropic mesh adaptation

Abstract

Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh adaptation for linear finite element solution of APME is discussed and numerical results for two dimensional examples are presented. The solution errors using anisotropic adaptive meshes show second order convergence.