Conservative flux recovery from the Q1 conforming finite element method on quadrilateral grids

So Hsiang Chou*, Songnian He, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Compared with standard Galerkin finite element methods, mixed methods for second-order elliptic problems give readily available flux approximation, but in general at the expense of having to deal with a more complicated discrete system. This is especially true when conforming elements are involved. Hence it is advantageous to consider a direct method when finding fluxes is just a small part of the overall modeling processes. The purpose of this article is to introduce a direct method combining the standard Galerkin Q1 conforming method with a cheap local flux recovery formula. The approximate flux resides in the lowest order Raviart-Thomas space and retains local conservation property at the cluster level. A cluster is made up of at most four quadrilaterals.

Original languageEnglish
Pages (from-to)104-127
Number of pages24
JournalNumerical Methods for Partial Differential Equations
Volume20
Issue number1
DOIs
StatePublished - 1 Jan 2004

Keywords

  • Local conservation property
  • Q1 conforming finite element
  • Raviart-Thomas space
  • Recovery technique

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