A primal-dual weak galerkin finite element method for fokker planck type equations

Chunmei Wang, Junping Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This paper presents a primal-dual weak Galerkin finite element method for a class of second order elliptic equations of Fokker-Planck type. The method is based on a variational form where all the derivatives are applied to the test functions so that no regularity is necessary for the exact solution of the model equation. The numerical scheme is designed by using locally constructed weak second order partial derivatives and the weak gradient commonly used in the weak Galerkin context. Optimal order of convergence is derived for the resulting numerical solutions. Numerical results are reported to demonstrate the performance of the numerical scheme.

Original languageEnglish
Pages (from-to)2632-2661
Number of pages30
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number5
DOIs
StatePublished - 2020

Keywords

  • Finite element methods
  • Fokker-Planck equation
  • Polytopal partitions
  • Primal-dual
  • Weak Galerkin
  • Weak Hessian
  • Weak gradient

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