Convergence analysis without regularity assumptions for multigrid algorithms based on SOR smoothing. (English) Zbl 0753.65093

Wang, Junping

SIAM J. Numer. Anal. 29, No. 4, 987-1001 (1992).

Convergence estimates for the standard multigrid algorithms based on successive overrelaxation (SOR) smoothing are established without regularity assumptions for symmetric and positive definite variational problems, and the results are applied to second order elliptic equations discretized by using finite element methods.

Reviewer: J.D.P.Donnelly (Oxford)

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
35J25	Boundary value problems for second-order elliptic equations

Keywords:

Convergence estimates; multigrid algorithms; successive overrelaxation; smoothing; second order elliptic equations; finite element methods