Superconvergence of the gradient approximation for weak Galerkin finite element methods on nonuniform rectangular partitions

Dan Li, Chunmei Wang, Junping Wang

Research output: Contribution to journalArticle

Abstract

This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of O(hr), 1.5≤r≤2, for the numerical gradient obtained from the lowest order weak Galerkin element consisting of piecewise linear and constant functions. For this numerical scheme, the optimal order of error estimate is O(h) for the gradient approximation. The superconvergence reveals a superior performance of the weak Galerkin finite element methods. Some computational results are included to numerically validate the superconvergence theory.

Original languageEnglish
Pages (from-to)396-417
Number of pages22
JournalApplied Numerical Mathematics
Volume150
DOIs
StatePublished - Apr 2020

Keywords

  • Finite element methods
  • Nonuniform rectangular partitions
  • Second order elliptic equations
  • Superconvergence
  • Weak Galerkin

Fingerprint Dive into the research topics of 'Superconvergence of the gradient approximation for weak Galerkin finite element methods on nonuniform rectangular partitions'. Together they form a unique fingerprint.

  • Cite this