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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2086-2099 |
| Number of pages | 14 |
| Journal | Computers and Mathematics with Applications |
| Volume | 75 |
| Issue number | 6 |
| DOIs | |
| State | Published - Mar 15 2018 |
| Externally published | Yes |
Keywords
- Adaptive mesh
- Anisotropic diffusion
- Anisotropic mesh adaptation
- Finite element
- Moving mesh
- Porous medium equation
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics