Dual Formulations of Mixed Finite Element Methods with Applications

Details Dual Formulations of Mixed Finite Element Methods with Applications Dual Formulations of Mixed Finite Element Methods with Applications

2010-12-17

arxiv.org/abs/1012.3929v4

Mathematics

Differential Geometry

Invited paper. Submitted. Version 4 has revisions and restructuring but same essential ideas

Scientific paper

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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