Dual formulations of mixed finite element methods with applications

Andrew Gillette, Chandrajit Bajaj

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.

Original languageEnglish (US)
Pages (from-to)1213-1221
Number of pages9
JournalCAD Computer Aided Design
Volume43
Issue number10
DOIs
StatePublished - Oct 1 2011
Externally publishedYes

Keywords

  • Discrete exterior calculus
  • Finite element method
  • Hodge star
  • Partial differential equations
  • Whitney forms

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

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