Details

BEM-based Finite Element Approaches on Polytopal Meshes

Lecture Notes in Computational Science and Engineering, Band 130

von: Steffen Weißer
42,79 €
Verlag:	Springer
Format:	PDF
Veröffentl.:	18.07.2019
ISBN/EAN:	9783030209612
Sprache:	englisch

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Beschreibungen

Titelbeschreibung

<div><p>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. </p>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.  </p><p>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. </p><p> </p><p> </p></div><div><div><br></div></div>

Inhaltsverzeichnis

1. Introduction.- 2. Finite element method on polytopal meshes.- 3. Interpolation of non-smooth functions and anisotropic polytopal meshes.- 4. Boundary integral equations and their approximations.- 5. Adaptive BEM-based finite element method.- 6. Developments of mixed and problem-adapted BEM-based FEM.<br>

Back cover copy

<div><p>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. </p>

<p>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.  </p>

<p>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. </p>

<p> </p><br></div>

Sonderbeitrag

State-of-the-art introduction, mathematical analysis and applications of the BEM-based FEM combined in one monograph. One of the first methods designed for the treatment of boundary value problems on polygonal and polyhedral meshes. All theoretical results and considerations are illustrated by numerous computational examples and experiments in 2D and 3D. Broad discussion on the regularity of isotropic as well as anisotropic polygonal and polyhedral meshes, and on the resulting properties.