Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur comp...

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Bibliographic Details
Published inarXiv.org
Main Authors Kalchev, Delyan Z, Vassilevski, Panayot S
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.04.2020
Subjects
Computer Science - Numerical Analysis
Discretization
Finite element method
Mathematics - Numerical Analysis
Preconditioning
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ISSN2331-8422
DOI10.48550/arxiv.1910.06986

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Summary:We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. These preconditioners are analyzed on the fine scale and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1910.06986