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BEM-based Finite Element Approaches on Polytopal Meshes

  • Steffen Weißer
Book

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 130)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Steffen Weißer
    Pages 1-16
  3. Steffen Weißer
    Pages 17-63
  4. Steffen Weißer
    Pages 141-176
  5. Back Matter
    Pages 223-246

About this book

Introduction

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

Authors and affiliations

  • Steffen Weißer
    • 1
  1. 1.FR MathematikUniversität des SaarlandesSaarbrückenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-20961-2
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-20960-5
  • Online ISBN 978-3-030-20961-2
  • Series Print ISSN 1439-7358
  • Series Online ISSN 2197-7100
  • Buy this book on publisher's site