Overview
- 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.
Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 130)
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About this book
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.
Keywords
- BEM-based FEM
- Trefftz-like basis functions
- Non-standard finite element method
- Polygonal mesh
- Polyhedral mesh
- Poincaré constant
- Quasi-interpolation
- Residual based error estimate
- Dual-weighted residual estimator
- Adaptive mesh refinement
- Anisotropic mesh
- Mixed finite element method
- Convection-dominated problem
- Boundary element method
- Nyström method
- Polygonal finite elements
Table of contents (6 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: BEM-based Finite Element Approaches on Polytopal Meshes
Authors: Steffen Weißer
Series Title: Lecture Notes in Computational Science and Engineering
DOI: https://doi.org/10.1007/978-3-030-20961-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-20960-5Published: 19 July 2019
Softcover ISBN: 978-3-030-20963-6Published: 14 August 2020
eBook ISBN: 978-3-030-20961-2Published: 18 July 2019
Series ISSN: 1439-7358
Series E-ISSN: 2197-7100
Edition Number: 1
Number of Pages: XVII, 246
Number of Illustrations: 46 b/w illustrations, 23 illustrations in colour
Topics: Computational Science and Engineering, Approximations and Expansions, Numerical Analysis