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Cover Art
Author Shaĭdurov, V. V.

Title Multigrid methods for finite elements / V.V. Shaidurov.

Published Dordrecht ; Boston : Kluwer Academic Publishers, [1995]


Location Call No. Status
Uniform title Mnogosetochnye metody konechnykh ėlementov. English
Physical description xiv, 331 pages : illustrations ; 25 cm.
Series Mathematics and its applications ; v. 318.
Mathematics and its applications (Kluwer Academic Publishers) ; v. 318.
Bibliography Includes bibliographical references (pages 313-326) and index.
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.
Summary In this book two rapidly developing fields are combined: that of finite element methods, and that of multigrid algorithms. At the theoretical level the rate of convergence is justified 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.
Subject Finite element method.
Multigrid methods (Numerical analysis)
Boundary value problems.
Mathematical physics.
Engineering mathematics.
ISBN 0792332903 (acid-free paper)