BEM-based Finite Element Approaches on Polytopal Meshes (Hardcover, 1st ed. 2019)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Lecture Notes in Computational Science and Engineering, 130
Release date:	July 2019
First published:	2019
Authors:	Steffen Weisser
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	246
Edition:	1st ed. 2019
ISBN-13:	978-3-03-020960-5
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers
LSN:	3-03-020960-1
Barcode:	9783030209605

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