Availability: Multilevel finite element approximation

Multilevel finite element approximation: theory and applications

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Bibliographic Details
Main Author:	Oswald, Peter (Author)
Format:	Book
Language:	English
Published:	Stuttgart Teubner 1994
Series:	Teubner-Skripten zur Numerik
Subjects:	Approximation theory Differential equations, Partial Finite element method Function spaces Funktionenraum Multi-level-Verfahren Finite-Elemente-Methode Multivariate Approximation
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006429595&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	160 S. graph. Darst.
ISBN:	3519027194

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Record in the Search Index

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adam_text	Contents 1 Introduction 9 2 Finite element approximation 12 2.1 Finite elements, multivariate splines, wavelets 12 2.1.1 Finite element subspaces 12 2.1.2 Spline spaces 20 2.1.3 Wavelets 22 2.2 Moduli of smoothness and K functionals 27 2.3 Jackson and Whitney inequalities 29 2.4 Bernstein inequalities and inverse estimates 33 2.5 Information on other approximation schemes 36 2.6 Constructive characterization of Besov spaces 37 3 Function spaces 41 3.1 Spaces on TLd 42 3.1.1 Fourier decomposition methods 42 3.1.2 Other techniques and spaces 44 3.2 Spaces on domains and extension 48 3.3 Spaces on manifolds and traces 52 3.4 Approximation spaces on polyhedral domains 53 3.4.1 Definition and general properties 54 3.4.2 Approximation theory in the A v q scale 57 3.4.3 Norms on V, and special representations 58 3.4.4 Extensions, traces, boundary conditions 61 3.4.5 Output: Decomposition norms in H 66 8 Contents 4 Applications to multilevel methods 70 4.1 The abstract Schwarz theory 70 4.2 Second order elliptic equations 84 4.2.1 The basic multilevel preconditioners 84 4.2.2 Nested refinement 92 4.2.3 Further developments and problems 96 4.3 The biharmonic problem 99 4.4 Domain decomposition and boundary element methods 101 4.5 Sparse grids 108 4.6 Nonconforming and mixed methods Ill 4.6.1 Splittings for nonconforming elements Ill 4.6.2 Mixed finite element methods 113 5 Error estimates and adaptivity 116 5.1 Traditional error estimates 117 5.2 h version and nonlinear approximation 117 5.3 Adaptive multilevel methods 125 5.4 More complicated approximation schemes 129 5.4.1 The h p version 130 5.4.2 Wavelet packets and compression • • 134 5.4.3 Approximation with long rectangles 137 References 139 Index 159
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series2	Teubner-Skripten zur Numerik
spellingShingle	Oswald, Peter Multilevel finite element approximation theory and applications Approximation theory Differential equations, Partial Finite element method Function spaces Funktionenraum (DE-588)4134834-5 gnd Multi-level-Verfahren (DE-588)4344428-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Multivariate Approximation (DE-588)4314108-0 gnd
subject_GND	(DE-588)4134834-5 (DE-588)4344428-3 (DE-588)4017233-8 (DE-588)4314108-0
title	Multilevel finite element approximation theory and applications
title_auth	Multilevel finite element approximation theory and applications
title_exact_search	Multilevel finite element approximation theory and applications
title_full	Multilevel finite element approximation theory and applications von Peter Oswald
title_fullStr	Multilevel finite element approximation theory and applications von Peter Oswald
title_full_unstemmed	Multilevel finite element approximation theory and applications von Peter Oswald
title_short	Multilevel finite element approximation
title_sort	multilevel finite element approximation theory and applications
title_sub	theory and applications
topic	Approximation theory Differential equations, Partial Finite element method Function spaces Funktionenraum (DE-588)4134834-5 gnd Multi-level-Verfahren (DE-588)4344428-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Multivariate Approximation (DE-588)4314108-0 gnd
topic_facet	Approximation theory Differential equations, Partial Finite element method Function spaces Funktionenraum Multi-level-Verfahren Finite-Elemente-Methode Multivariate Approximation
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006429595&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT oswaldpeter multilevelfiniteelementapproximationtheoryandapplications

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