Higher-dimensional nonnested multigrid methods. (English) Zbl 0772.65077
The paper deals with nonnested multigrid methods for elliptic boundary problems (model problem is a source problem with Dirichlet type boundary conditions) in dimension 3 or more. For sequences of triangulations nondegeneracy is ensured by introducing conditions of quasiuniformity and refinement.
A multigrid scheme involving Lagrange type finite elements is introduced. Discussions of stability and convergence are based upon interpolation techniques and the results of J. H. Bramble, J. E. Pasciak and J. Xu [Math. Comput. 56, No. 193, 1-34 (1991; Zbl 0718.65081)]. It is also shown that, under certain conditions, the schemes are of optimal work order, relating to R. E. Bank and T. Dupont [Math. Comput. 36, 35-51 (1981; Zbl 0466.65059)].
A multigrid scheme involving Lagrange type finite elements is introduced. Discussions of stability and convergence are based upon interpolation techniques and the results of J. H. Bramble, J. E. Pasciak and J. Xu [Math. Comput. 56, No. 193, 1-34 (1991; Zbl 0718.65081)]. It is also shown that, under certain conditions, the schemes are of optimal work order, relating to R. E. Bank and T. Dupont [Math. Comput. 36, 35-51 (1981; Zbl 0466.65059)].
Reviewer: S.L.Svensson (Lund)
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 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 |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
nonnested multigrid methods; quasiuniformity; refinement; finite elements; stability; convergenceReferences:
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