Anisotropic mesh adaptation for finite element solution of Anisotropic Porous Medium Equation

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1 Scopus citations

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 languageEnglish (US)
Pages (from-to)2086-2099
Number of pages14
JournalComputers and Mathematics with Applications
Volume75
Issue number6
DOIs
StatePublished - Mar 15 2018
Externally publishedYes

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

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