The Mathematical Theory of Finite Element Methods : Texts in Applied Mathematics / Susanne C. Brenner & L. Ridgway Scott

By:

Brenner, Susanne

Contributor(s):

Scott, L. Ridgway

Material type: Text

TextLanguage: English Publication details: New Delhi : Springer India Pvt Ltd , 2011 .Edition: 3rdDescription: 397 pISBN:

9781441926111

Subject(s):

Sobolev space algorithm algorithms construction finite element method finite elements functional analysis numerical analysis operator

DDC classification:

515.353 BRE

Contents:

Table of contents (15 chapters) Front Matter Pages i-xvii Basic Concepts Pages 1-22 Sobolev Spaces Pages 23-47 Variational Formulation of Elliptic Boundary Value Problems Pages 49-67 The Construction of a Finite Element Space Pages 69-92 Polynomial Approximation Theory in Sobolev Spaces Pages 93-127 n-Dimensional Variational Problems Pages 129-154 Finite Element Multigrid Methods Pages 155-173 Additive Schwarz Preconditioners Pages 175-214 Max—norm Estimates Pages 215-240 Adaptive Meshes Pages 241-269 Variational Crimes Pages 271-309 Applications to Planar Elasticity Pages 311-329 Mixed Methods Pages 331-354 Iterative Techniques for Mixed Methods Pages 355-370 Applications of Operator-Interpolation Theory Pages 371-381 Back Matter Pages 383-398

Summary: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAMwillpublishtextbookssuitableforuseinadvancedundergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Preface to the Third Edition This edition contains four new sections on the following topics: the BDDC domain decomposition preconditioner (Section 7.8), a convergent ad- tive algorithm (Section 9.5), interior penalty methods (Section 10.5) and 1 Poincar´ e-Friedrichs inequalities for piecewise W functions (Section 10.6).

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Holdings
Item type	Current library	Collection	Call number	Status	Barcode
General Books	CUTN Central Library Sciences	Non-fiction	515.353 BRE (Browse shelf(Opens below))	Available	50354

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Previous	515.352 NAN Ordinary Differential Equations : Principles and Applications /	515.352 NAN Ordinary Differential Equations : Principles and Applications /	515.353 AMA An elementary course in partial differential equations /	515.353 BRE The Mathematical Theory of Finite Element Methods : Texts in Applied Mathematics /	515.353 GAL An introduction to the mathematical theory of the Navier-Stokes equations /	515.353 GRO The Yang-Mills heat equation with finite action in three dimensions /	515.353 HAT Partial differential equations : Methods, applications and theories /	Next

Table of contents (15 chapters)
Front Matter
Pages i-xvii
Basic Concepts
Pages 1-22
Sobolev Spaces
Pages 23-47
Variational Formulation of Elliptic Boundary Value Problems
Pages 49-67
The Construction of a Finite Element Space
Pages 69-92
Polynomial Approximation Theory in Sobolev Spaces
Pages 93-127
n-Dimensional Variational Problems
Pages 129-154
Finite Element Multigrid Methods
Pages 155-173
Additive Schwarz Preconditioners
Pages 175-214
Max—norm Estimates
Pages 215-240
Adaptive Meshes
Pages 241-269
Variational Crimes
Pages 271-309
Applications to Planar Elasticity
Pages 311-329
Mixed Methods
Pages 331-354
Iterative Techniques for Mixed Methods
Pages 355-370
Applications of Operator-Interpolation Theory
Pages 371-381
Back Matter
Pages 383-398

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAMwillpublishtextbookssuitableforuseinadvancedundergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Preface to the Third Edition This edition contains four new sections on the following topics: the BDDC domain decomposition preconditioner (Section 7.8), a convergent ad- tive algorithm (Section 9.5), interior penalty methods (Section 10.5) and 1 Poincar´ e-Friedrichs inequalities for piecewise W functions (Section 10.6).

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