Weißer BEM-based Finite Element Approaches on Polytopal Meshes

1. Auflage 2019
ISBN: 978-3-030-20961-2
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 130, 246 Seiten, eBook

Reihe: Lecture Notes in Computational Science and Engineering

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.

Zielgruppe

Research

Autoren/Hrsg.

Weißer, Steffen

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.