Liu, Fang; Zhou, Aihui Localizations and parallelizations for two-scale finite element discretizations. (English) Zbl 1141.65079 Commun. Pure Appl. Anal. 6, No. 3, 757-773 (2007). 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. Reviewer: Ariadna Lucia Pletea (Iaşi) Cited in 3 Documents MSC: 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 Keywords:finite element; parallel algorithms; localization; tensor product; two-scale discretization; elliptic boundary value problem PDFBibTeX XMLCite \textit{F. Liu} and \textit{A. Zhou}, Commun. Pure Appl. Anal. 6, No. 3, 757--773 (2007; Zbl 1141.65079) Full Text: DOI