BEM-based Finite Element Approaches on Polytopal Meshes: 130 (Lecture Notes in Computational Science and Engineering) - Softcover

Buch 103 von 111: Lecture Notes in Computational Science and Engineering

Weißer, Steffen

 
9783030209636: BEM-based Finite Element Approaches on Polytopal Meshes: 130 (Lecture Notes in Computational Science and Engineering)
Softcover
ISBN 10: 3030209636 ISBN 13: 9783030209636
Verlag: Springer, 2020

Inhaltsangabe

This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes.

The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments.  

Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.

 


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This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes.

The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments.  

Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.

 


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Verlag
Springer
Erscheinungsdatum
2020
Sprache
Englisch
ISBN 10 
3030209636
ISBN 13 
9783030209636
Einband
Tapa blanda
Auflage
1
Anzahl der Seiten
264
Kontakt zum Hersteller
Nicht verfügbar
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9783030209605: BEM-based Finite Element Approaches on Polytopal Meshes: 130 (Lecture Notes in Computational Science and Engineering)

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Verlag: Springer, 2019
Hardcover