A generalization for stable mixed finite elements

Andrew Gillette, Chandrajit Bajaj

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

Mixed finite element methods solve a PDE involving two or more variables. In typical problems from electromagnetics and electrodiffusion, the degrees of freedom associated to the different variables are stored on both primal and dual domain meshes and a discrete Hodge star is used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the model and numerical stability of a finite element method. We also show how to define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods.

Original languageEnglish (US)
Title of host publicationProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10
Pages41-50
Number of pages10
DOIs
StatePublished - Oct 25 2010
Externally publishedYes
Event14th ACM Symposium on Solid and Physical Modeling, SPM'10 - Haifa, Israel
Duration: Sep 1 2010Sep 3 2010

Publication series

NameProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10

Other

Other14th ACM Symposium on Solid and Physical Modeling, SPM'10
CountryIsrael
CityHaifa
Period9/1/109/3/10

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Algebra and Number Theory
  • Geometry and Topology

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  • Cite this

    Gillette, A., & Bajaj, C. (2010). A generalization for stable mixed finite elements. In Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10 (pp. 41-50). (Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10). https://doi.org/10.1145/1839778.1839785