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Mixed Finite Element Methods and Applications [electronic resource] / by Daniele Boffi, Franco Brezzi, Michel Fortin.

By: Boffi, Daniele [author.].
Contributor(s): Brezzi, Franco [author.] | Fortin, Michel [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Series in Computational Mathematics: 44Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013Description: XIV, 685 p. 67 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642365195.Subject(s): Mathematics | Computer science -- Mathematics | Computer science | Mechanics, applied | Mathematics | Computational Mathematics and Numerical Analysis | Computational Science and Engineering | Theoretical and Applied MechanicsDDC classification: 518 | 518 Online resources: Click here to access online
Contents:
Preface -- Variational Formulations and Finite Element Methods -- Function Spaces and Finite Element Approximations -- Algebraic Aspects of Saddle Point Problems -- Saddle Point Problems in Hilbert spaces -- Approximation of Saddle Point Problems -- Complements: Stabilisation Methods, Eigenvalue Problems -- Mixed Methods for Elliptic Problems -- Incompressible Materials and Flow Problems -- Complements on Elasticity Problems -- Complements on Plate Problems -- Mixed Finite Elements for Electromagnetic Problems -- Index.        .
In: Springer eBooksSummary: Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem,  plate problems, elasticity and electromagnetism.
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Preface -- Variational Formulations and Finite Element Methods -- Function Spaces and Finite Element Approximations -- Algebraic Aspects of Saddle Point Problems -- Saddle Point Problems in Hilbert spaces -- Approximation of Saddle Point Problems -- Complements: Stabilisation Methods, Eigenvalue Problems -- Mixed Methods for Elliptic Problems -- Incompressible Materials and Flow Problems -- Complements on Elasticity Problems -- Complements on Plate Problems -- Mixed Finite Elements for Electromagnetic Problems -- Index.        .

Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem,  plate problems, elasticity and electromagnetism.

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