Multigrid Methods for Finite Elements

V. V. Shaidurov

ISBN 10: 9048145066 / ISBN 13: 9789048145065

Editore: Springer Netherlands, 2010

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Druck auf Anfrage Neuware - Printed after ordering - Multigrid Methods for Finite Elements combines two rapidly developing fields: finite element methods, and multigrid algorithms. At the theoretical level, Shaidurov justifies the rate of convergence of various multigrid algorithms for self-adjoint and non-self-adjoint problems, positive definite and indefinite problems, and singular and spectral problems. At the practical level these statements are carried over to detailed, concrete problems, including economical constructions of triangulations and effective work with curvilinear boundaries, quasilinear equations and systems. Great attention is given to mixed formulations of finite element methods, which allow the simplification of the approximation of the biharmonic equation, the steady-state Stokes, and Navier--Stokes problems.

Codice articolo 9789048145065

Dati bibliografici

• Titolo: Multigrid Methods for Finite Elements
• Editore: Springer Netherlands
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 9048145066
• ISBN 13: 9789048145065
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

Multigrid Methods for Finite Elements combines two rapidly developing fields: finite element methods, and multigrid algorithms. At the theoretical level, Shaidurov justifies the rate of convergence of various multigrid algorithms for self-adjoint and non-self-adjoint problems, positive definite and indefinite problems, and singular and spectral problems. At the practical level these statements are carried over to detailed, concrete problems, including economical constructions of triangulations and effective work with curvilinear boundaries, quasilinear equations and systems. Great attention is given to mixed formulations of finite element methods, which allow the simplification of the approximation of the biharmonic equation, the steady-state Stokes, and Navier--Stokes problems.

Contenuti

Preface. Introduction. 1. Elliptic boundary-value problems and Bubnov--Galerkin method. 2. General properties of finite elements. 3. On the convergence of approximate solutions. 4. General description of multigrid algorithms. 5. Realization of the algorithms for second-order equations. 6. Solving nonlinear problems and systems of equations. Bibliography. Index.