Finite élements

Theory, fast solvers, and applications in solid mechanics

Dietrich Braess

354 pages, parution le 25/10/2001 (2^eme édition)

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Résumé

The most inportant application of the finite element method is the numerical solution of elliptical partial differential equations. This is covered in depth in this book. It is a textbook for graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite elements for engineering or mathematics applications.

Table of Contents

	Preface to the Second English Edition
	Preface to the First English Edition
	Preface to the German Edition
	Notation
Ch. I	Introduction	1
1	Examples and Classification of PDE's	2
2	The Maximum Principle	12
3	Finite Difference Methods	16
4	A Convergence Theory for Difference Methods	22
Ch. II	Conforming Finite Elements	27
1	Sobolev Spaces	28
2	Variational Formulation of Elliptic Boundary-Value Problems of Second Order	34
3	The Neumann Boundary-Value Problem. A Trace Theorem	44
4	The Ritz-Gelerkin Method and Some Finite Elements	53
5	Some Standard Finite Elements	60
6	Approximation Properties	76
7	Error Bounds for Elliptic Problems of Second Order	89
8	Computational Considerations	97
Ch. III	Nonconforming and Other Methods	105
1	Abstract Lemmas and a Simple Boundary Approximation	106
2	Isoparametric Elements	117
3	Further Tools from Functional Analysis	122
4	Saddle Point Problems	129
5	Mixed Methods for the Poisson Equation	143
6	The Stokes Equation	154
7	Finite Elements for the Stokes Problem	159
8	A Posteriori Error Estimates	169
Ch. IV	The Conjugate Gradient Method	177
1	Classical Iterative Methods for Solving Linear Systems	178
2	Gradient Methods	187
3	Conjugate Gradient and the Minimal Residual Method	192
4	Preconditioning	201
5	Saddle Point Problems	212
Ch. V	Multigrid Methods	216
1	Multigrid Methods for Variational Problems	217
2	Convergence of Multigrid Methods	228
3	Convergence for Several Levels	239
4	Nested Iteration	246
5	Multigrid Analysis via Space Decomposition	252
6	Nonlinear Problems	263
Ch. VI	Finite Elements in Solid Mechanics	270
1	Introduction to Elasticity Theory	270
2	Hyperelastic Materials	281
3	Linear Elasticity Theory	284
4	Membranes	304
5	Beams and Plates: The Kirchhoff Plate	312
6	The Mindlin-Reissner Plate	324
	References	337
	Some Additional Books on Finite Elements	347
	Index	348

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Dietrich Braess
Parution	25/10/2001
Édition	2^eme édition
Nb. de pages	354
Format	15 x 22,8
Couverture	Broché
Poids	519g
Intérieur	Noir et Blanc
EAN13	9780521011952
ISBN13	978-0-521-01195-2