A modified primal-dual weak galerkin finite element method for second order elliptic equations in non-divergence form

Chunmei Wang

Research output: Contribution to journalArticlepeer-review

Abstract

A modified primal-dual weak Galerkin (M-PDWG) finite element method is designed for the second order elliptic equation in non-divergence form. Compared with the existing PDWG methods proposed in [6], the system of equations resulting from the M-PDWG scheme could be equivalently simplified into one equation involving only the primal variable by eliminating the dual variable (Lagrange multiplier). The resulting simplified system thus has significantly fewer degrees of freedom than the one resulting from existing PDWG scheme. Optimal order error estimates are derived for the numerical approximations in the discrete H2-norm, H1-norm and L2-norm respectively. Extensive numerical results are demonstrated for both the smooth and non-smooth coefficients on convex and non-convex domains to verify the accuracy of the theory developed in this paper.

Original languageEnglish
Pages (from-to)500-523
Number of pages24
JournalInternational Journal of Numerical Analysis and Modeling
Volume18
Issue number4
StatePublished - 2021

Keywords

  • Cordès condition
  • Finite element methods
  • Non-divergence form
  • Polyhedral meshes
  • Primal-dual
  • Weak Galerkin

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