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Cascadic multigrid method for elliptic problems. (English) Zbl 0943.65143

The cascadic multigrid method introduced by F. A. Bornemann and P. Deuflhard [Numer. Math. 75, No. 2, 135-152 (1996; Zbl 0873.65107)] is investigated. It requires no coarse grid corrections and more iterations on coarser levels so as to obtain less iterations on finer levels. Convergence results for conforming and nonconforming finite elements are shown. The cascadic multigrid is extended to the plate bending problem. In contrast to second-order problems the conjugate gradient method only gives nearly optimal complexity.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65Y20 Complexity and performance of numerical algorithms
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Citations:

Zbl 0873.65107
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