Multigrid Methods for Finite Elements by V.V. Shaidurov (English) Paperback Book

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Multigrid Methods for Finite Elements by V.V. Shaidurov

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.

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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.

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Table of Contents

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.

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Long Description

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.

Details ISBN9048145066 Author V.V. Shaidurov Publisher Springer Year 2010 ISBN-10 9048145066 ISBN-13 9789048145065 Format Paperback Imprint Springer Place of Publication Dordrecht Country of Publication Netherlands DEWEY 518.25 Edition 1st Short Title MULTIGRID METHODS FOR FINITE E Language English Media Book Series Number 318 Pages 334 Illustrations XIV, 334 p. Series Mathematics and Its Applications Publication Date 2010-12-15 Edition Description Softcover reprint of hardcover 1st ed. 1995 Alternative 9780792332909 Audience Professional & Vocational Country of Origin NL Product Class Description Mathematics
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