Superconvergence of numerical gradient for weak Galerkin finite element methods on nonuniform Cartesian partitions in three dimensions

Dan Li, Yufeng Nie, Chunmei Wang

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

A superconvergence error estimate for the gradient approximation of the second order elliptic problem in three dimensions is analyzed by using weak Galerkin finite element scheme on the uniform and non-uniform cubic partitions. Due to the loss of the symmetric property from two dimensions to three dimensions, this superconvergence result in three dimensions is not a trivial extension of the recent superconvergence result in two dimensions Li et al. (0000) from rectangular partitions to cubic partitions. The error estimate for the numerical gradient in the L2-norm arrives at a superconvergence order of O(hr)(1.5≤r≤2) when the lowest order weak Galerkin finite elements consisting of piecewise linear polynomials in the interior of the elements and piecewise constants on the faces of the elements are employed. A series of numerical experiments are illustrated to confirm the established superconvergence theory in three dimensions.

Original languageEnglish
Pages (from-to)905-928
Number of pages24
JournalComputers and Mathematics with Applications
Volume78
Issue number3
DOIs
StatePublished - Aug 1 2019

Keywords

  • Non-uniform cubic partitions
  • Second order elliptic problem
  • Superconvergence
  • Three dimensions
  • Weak Galerkin finite element method

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