BEM-based Finite Element Approaches on Polytopal Meshes - Steffen Weißer

BEM-based Finite Element Approaches on Polytopal Meshes

(Autor)

Buch | Softcover
XVII, 246 Seiten
2020 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-20963-6 (ISBN)
106,99 inkl. MwSt

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.

 


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.

Erscheinungsdatum
Reihe/Serie Lecture Notes in Computational Science and Engineering
Zusatzinfo XVII, 246 p. 69 illus., 23 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 409 g
Themenwelt Mathematik / Informatik Informatik
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Schlagworte Adaptive mesh refinement • Anisotropic mesh • BEM-based FEM • Boundary element method • Convection-dominated problem • Dual-weighted residual estimator • Mixed finite element method • Non-standard finite element method • Nyström method • Nyström method • Poincaré constant • Poincaré constant • Polygonal finite elements • Polygonal mesh • polyhedral mesh • Quasi-interpolation • Residual based error estimate • Trefftz-like basis functions
ISBN-10 3-030-20963-6 / 3030209636
ISBN-13 978-3-030-20963-6 / 9783030209636
Zustand Neuware
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