BEM-based Finite Element Approaches on Polytopal Meshes. 1st ed. 2019

種類:

電子ブック

責任表示:

by Steffen Weißer

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Weißer, Steffen.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Computational Science and Engineering ; 130

ISBN:

9783030209612 [303020961X]    

注記:

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.
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 an

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