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Dynamic parallel Galerkin domain decomposition procedures with grid modification for parabolic equation. (English) Zbl 1225.65096
The authors consider a diffusion-reaction parabolic equation in d (3) dimensions and continue their development of dynamic parallel Galerkin domain decomposition methods based on the work of C. N. Dawson and T. F. Dupont [Math. Comput. 58, No. 197, 21–34 (1992; Zbl 0746.65072)] and the former work by K. Ma, T. Sun and D. Yang, [Numer. Methods Partial Differ. Equations 25, No. 5, 1167–1194 (2009; Zbl 1173.65061)]. Here dynamically changing decompositions, grids in subdomains, and finite element spaces are possible, the aim being a better resolution in problems with sharp fronts and layers. They use implicit Galerkin in the subdomains and (two variants of) explicit flux calculations at inter-domain boundaries – from where a time step restriction arises. The bulk of the paper is devoted to a priori error estimates. The paper concludes with a report on numerical experiments on two-dimensional problems using bilinear elements which shows second order convergence, somewhat better L 2 errors than the method of Ma, Sun, and Yang [loc. cit.], but on the cost of decisively more computing time.
MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M55Multigrid methods; domain decomposition (IVP of PDE)
35K57Reaction-diffusion equations
65Y05Parallel computation (numerical methods)
65M50Mesh generation and refinement (IVP of PDE)