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Two-scale finite element discretizations for partial differential equations. (English) Zbl 1100.65101
The authors propose a finite element discretization for elliptic equations on a rectangular parallelpiped. The method consists of solving the problem on a coarse grid and then sequentially with a grid which is fine in each coordinate direction. A more accurate solution is obtained by extrapolating these results. The corresponding method for two-dimensional problems was analyzed by C. Pflaum and A. Zhou [J. Numer. Math. 84, 327–350 (1999; Zbl 0942.65122)].

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