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Sparse grids. (English) Zbl 0763.65091
Parallel algorithms for partial differential equations, Proc. 6th GAMM- Semin., Kiel/Ger. 1990, Notes Numer. Fluid Mech. 31, 241-251 (1991).
[For the entire collection see Zbl 0741.00060.]
This is a well written introduction into the sparse grid approach. That approach is useful for interpolation, integration and solution of partial differential equations. It starts from a hierarchical basis the elements of which are selected in accordance with their (estimated) contribution to the interpolation error, and leads to a drastical reduction of the dimension of the finite element method space needed to reach a given accuracy. The method also works in 3 dimensions and gives rise to an additional possibility to parallelize the multigrid method.

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs