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TitleMixed and Hybrid Finite Element Methods [electronic resource] / edited by Franco Brezzi, Michel Fortin
ImprintNew York, NY : Springer New York, 1991
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Descript IX, 350p. 65 illus. online resource


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


I: Variational Formulations and Finite Element Methods -- ยง1. Classical Methods -- ยง2. Model Problems and Elementary Properties of Some Functional Spaces -- ยง3. Duality Methods -- ยง4. Domain Decomposition Methods, Hybrid Methods -- ยง5. Augmented Variational Formulations -- ยง6. Transposition Methods -- ยง7. Bibliographical remarks -- II: Approximation of Saddle Point Problems -- ยง1. Existence and Uniqueness of Solutions -- ยง2. Approximation of the Problem -- ยง3. Numerical Properties of the Discrete Problem -- ยง4. Solution by Penalty Methods, Convergence of Regularized Problems -- ยง5. Iterative Solution Methods. Uzawaโ{128}{153}s Algorithm -- ยง6. Concluding Remarks -- III: Function Spaces and Finite Element Approximations -- ยง1. Properties of the spaces Hs(?) and H(div; ?) -- ยง2. Finite Element Approximations of H1(?) and H2(?) -- ยง3. Approximations of H (div; ?) -- ยง4. Concluding Remarks -- IV: Various Examples -- ยง1. Nonstandard Methods for Dirichletโ{128}{153}s Problem -- ยง2. Stokes Problem -- ยง3. Elasticity Problems -- ยง4. A Mixed Fourth-Order Problem -- ยง5. Dual Hybrid Methods for Plate Bending Problems -- V: Complements on Mixed Methods for Elliptic Problems -- ยง1. Numerical Solutions -- ยง2. A Brief Analysis of the Computational Effort -- ยง3. Error Analysis for the Multiplier -- ยง4. Error Estimates in Other Norms -- ยง5. Application to an Equation Arising from Semiconductor Theory -- ยง6. How Things Can Go Wrong -- ยง7. Augmented Formulations -- VI: Incompressible Materials and Flow Problems -- ยง1. Introduction -- ยง2. The Stokes Problem as a Mixed Problem -- ยง3. Examples of Elements for Incompressible Materials -- ยง4. Standard Techniques of Proof for the inf-sup Condition -- ยง5. Macroelement Techniques and Spurious Pressure Modes -- ยง6. An Alternative Technique of Proof and Generalized Taylor-Hood Element -- ยง7. Nearly Incompressible Elasticity, Reduced Integration Methods and Relation with Penalty Methods -- ยง8. Divergence-Free Basis, Discrete Stream Functions -- ยง9. Other Mixed and Hybrid Methods for Incompressible Flows -- VII: Other Applications -- ยง1. Mixed Methods for Linear Thin Plates -- ยง2. Mixed Methods for Linear Elasticity Problems -- ยง3. Moderately Thick Plates -- References

Mathematics Numerical analysis Mathematics Numerical Analysis


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