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Localizations and parallelizations for two-scale finite element discretizations. (English) Zbl 1141.65079
The authors propose some new local and parallel algorithms for finite element computation. The main idea of new algorithms is to use a coarse grid to approximate the low frequencies and then to use some partially fine grids to correct the resulted residue (that contains mostly high frequencies) by some local procedures. The algorithms are proposed and analyzed in this paper for elliptic boundary value problem.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65Y05 Parallel numerical computation
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