Multigrid Methods for Finite Elements
By: by V. V. Shaidurov
Series: Mathematics and Its Applications -- 318; Mathematics and Its Applications -- 318
Publisher: Springer Netherlands
Published: 1995
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 334
ISBN-13: 9789048145065; 9789401585279
Subjects: Mathematics; Differential equations, partial; Algorithms; Computer science; Engineering mathematics
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.
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