Mixed and Hybrid Finite Element Methods [Paperback]

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.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.- ?1. Classical Methods.- ?2. Model Problems and Elementary Properties of Some Functional Spaces.- ?3. Duality Methods.- 3.1. Generalities.- 3.2. Examples for symmetric problems.- 3.3. Duality methods for nonsymmetric bilinear forms.- ?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.- 1.1. Quadratic problems under linear constraints.- 1.2. Extensions of existence and uniqueness results.- ?2. Approximation of the Problem.- 2.1. Basic results.- 2.2. Error estimates for the basic problem.- 2.3. The inf-sup condition: criteria.- 2.4. Extensions of error estimates.- 2.5. Various generalizations of error estimates.- 2.6. Perturbations of the problem, nonconforming methods.- 2.7. Dual error estimates.- ?3. Numerical Properties of the Discrete Problem.- 3.1. The matrix form of the discrete problem.- 3.2. Eigenvalue problem associated with the inf-sup condition.- 3.3. Is the inf-sup condition so important?.- ?4. Solul3-