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BEM-based Finite Element Approaches on Polytopal Meshes
Af: Steffen Weisser Engelsk Paperback
SPAR
kr 96
BEM-based Finite Element Approaches on Polytopal Meshes
Af: Steffen Weisser Engelsk Paperback

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.

 


Produktdetaljer
Sprog: Engelsk
Sider: 246
ISBN-13: 9783030209636
Indbinding: Paperback
Udgave:
ISBN-10: 3030209636
Udg. Dato: 14 aug 2020
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Oplagsdato: 14 aug 2020
Forfatter(e): Steffen Weisser
Forfatter(e) Steffen Weisser


Kategori Differentialregning & ligninger


Sprog Engelsk


Indbinding Paperback


Sider 246


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm


Udg. Dato 14 aug 2020


Oplagsdato 14 aug 2020

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