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Étude algébrique d’une méthode multigrille pour quelques problèmes de frontière libre. (French) Zbl 0543.65044

Using the algebraic study of convergence of multigrid methods for equations introduced by A. Brandt, we obtain a bound on the two-level asymptotic convergence factor of the multigrid method for variational inequalities proposed recently by the author [Appl. Math. Optimization 11, 77-95 (1984; Zbl 0539.65046)]. The results can be also applied to multigrid methods for elliptic problems with a complicated boundary which is poorly approximated by coarse grids. We give a simplified proof of some of A. Brandt’s results, which permits some extensions.

MSC:

65K10 Numerical optimization and variational techniques
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
35R35 Free boundary problems for PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs

Citations:

Zbl 0539.65046
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