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Catalogue Information
Field name	Details
Dewey Class	004
Title	BEM-based Finite Element Approaches on Polytopal Meshes ([EBook]) / by Steffen Weißer.
Author	Weißer, Steffen
Other name(s)	SpringerLink (Online service)
Publication	Cham : Springer International Publishing , 2019.
Physical Details	XVII, 246 pages, 69 illus., 23 illus. in color. : online resource.
Series	Lecture Notes in Computational Science and Engineering ; 130
ISBN	9783030209612
Summary Note	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. .:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-20961-2
Links to Related Works	Subject References: Approximation theory . Approximations and Expansions . Computational Science and Engineering . Computer mathematics . Numerical Analysis . Authors: author . Weißer, Steffen . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Computational Science and Engineering . Classification: 004 . 004 (DDC 23) .

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BEM-based Finite Element Approaches on Polytopal Meshes

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