A hybridized weak Galerkin finite element method for the biharmonic equation

Chunmei Wang, Junping Wang

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An error estimate of optimal order is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknowns associated with the interior variables on each element, yielding a significantly reduced system of linear equations for unknowns on the element interfaces.

Original languageEnglish
Pages (from-to)302-317
Number of pages16
JournalInternational Journal of Numerical Analysis and Modeling
Volume12
Issue number2
StatePublished - 2015

Keywords

  • Biharmonic problems
  • Finite element methods
  • Hybridized weak galerkin
  • Weak galerkin
  • Weak hessian

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