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Dual formulations of mixed finite element methods with applications

Authors
Publisher
Elsevier Ltd
Publication Date
Volume
43
Issue
10
Identifiers
DOI: 10.1016/j.cad.2011.06.017
Keywords
  • Discrete Exterior Calculus
  • Finite Element Method
  • Partial Differential Equations
  • Whitney Forms
  • Hodge Star

Abstract

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.

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