UID:
almahu_9947362838702882
Format:
IX, 350p. 65 illus.
,
online resource.
ISBN:
9781461231721
Series Statement:
Springer Series in Computational Mathematics, 15
Content:
Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.
Note:
I: Variational Formulations and Finite Element Methods -- §1. Classical Methods -- §2. Model Problems and Elementary Properties of Some Functional Spaces -- §3. Duality Methods -- §4. Domain Decomposition Methods, Hybrid Methods -- §5. Augmented Variational Formulations -- §6. Transposition Methods -- §7. Bibliographical remarks -- II: Approximation of Saddle Point Problems -- §1. Existence and Uniqueness of Solutions -- §2. Approximation of the Problem -- §3. Numerical Properties of the Discrete Problem -- §4. Solution by Penalty Methods, Convergence of Regularized Problems -- §5. Iterative Solution Methods. Uzawa’s Algorithm -- §6. Concluding Remarks -- III: Function Spaces and Finite Element Approximations -- §1. Properties of the spaces Hs(?) and H(div; ?) -- §2. Finite Element Approximations of H1(?) and H2(?) -- §3. Approximations of H (div; ?) -- §4. Concluding Remarks -- IV: Various Examples -- §1. Nonstandard Methods for Dirichlet’s Problem -- §2. Stokes Problem -- §3. Elasticity Problems -- §4. A Mixed Fourth-Order Problem -- §5. Dual Hybrid Methods for Plate Bending Problems -- V: Complements on Mixed Methods for Elliptic Problems -- §1. Numerical Solutions -- §2. A Brief Analysis of the Computational Effort -- §3. Error Analysis for the Multiplier -- §4. Error Estimates in Other Norms -- §5. Application to an Equation Arising from Semiconductor Theory -- §6. How Things Can Go Wrong -- §7. Augmented Formulations -- VI: Incompressible Materials and Flow Problems -- §1. Introduction -- §2. The Stokes Problem as a Mixed Problem -- §3. Examples of Elements for Incompressible Materials -- §4. Standard Techniques of Proof for the inf-sup Condition -- §5. Macroelement Techniques and Spurious Pressure Modes -- §6. An Alternative Technique of Proof and Generalized Taylor-Hood Element -- §7. Nearly Incompressible Elasticity, Reduced Integration Methods and Relation with Penalty Methods -- §8. Divergence-Free Basis, Discrete Stream Functions -- §9. Other Mixed and Hybrid Methods for Incompressible Flows -- VII: Other Applications -- §1. Mixed Methods for Linear Thin Plates -- §2. Mixed Methods for Linear Elasticity Problems -- §3. Moderately Thick Plates -- References.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9781461278245
Language:
English
DOI:
10.1007/978-1-4612-3172-1
URL:
http://dx.doi.org/10.1007/978-1-4612-3172-1
