Anisotropic Mesh Adaptation for Finite Element Solution of Anisotropic Porous Medium Equation
For researchers in computational fluid dynamics or porous media, this provides a method to improve accuracy in anisotropic diffusion problems, though it is an incremental extension of existing techniques.
The paper extends the Porous Medium Equation to anisotropic porous media, derives an analytical solution, and demonstrates that anisotropic mesh adaptation achieves second-order convergence in finite element solutions.
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.