A generalization for stable mixed finite elements

Andrew Gillette, Chandrajit Bajaj

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

6 Citations (Scopus)

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 - 2010
Externally publishedYes
Event14th ACM Symposium on Solid and Physical Modeling, SPM'10 - Haifa, Israel
Duration: Sep 1 2010Sep 3 2010

Other

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

Fingerprint

Mixed Finite Elements
Stars
Star
Mesh
Finite element method
Interpolation Function
Information Transfer
Mixed Methods
Mixed Finite Element Method
Convergence of numerical methods
Numerical Stability
Interpolation
Degree of freedom
Finite Element Method
Generalization
Model

ASJC Scopus subject areas

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

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) https://doi.org/10.1145/1839778.1839785

A generalization for stable mixed finite elements. / Gillette, Andrew; Bajaj, Chandrajit.

Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10. 2010. p. 41-50.

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

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, 14th ACM Symposium on Solid and Physical Modeling, SPM'10, Haifa, Israel, 9/1/10. https://doi.org/10.1145/1839778.1839785
Gillette A, Bajaj C. A generalization for stable mixed finite elements. In Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10. 2010. p. 41-50 https://doi.org/10.1145/1839778.1839785
Gillette, Andrew ; Bajaj, Chandrajit. / A generalization for stable mixed finite elements. Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10. 2010. pp. 41-50
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