Multigrid Methods for Finite Elements

✍ Scribed by V. V. Shaidurov (auth.)

• Publisher: Springer Netherlands
• Year: 1995
• Tongue: English
• Leaves: 344
• Series: Mathematics and Its Applications 318
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XIV
Elliptic boundary-value problems and Bubnov-Galerkin method....Pages 1-36
General properties of finite elements....Pages 37-74
On the convergence of approximate solutions....Pages 75-116
General description of multigrid algorithms....Pages 117-205
Realization of the algorithms for second-order equations....Pages 207-249
Solving nonlinear problems and systems of equations....Pages 251-311
Back Matter....Pages 313-334

✦ Subjects

Applications of Mathematics; Appl.Mathematics/Computational Methods of Engineering; Computational Mathematics and Numerical Analysis; Algorithms; Partial Differential Equations