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Zbl 1225.65096
Sun, Tongjun; Ma, Keying
Dynamic parallel Galerkin domain decomposition procedures with grid modification for parabolic equation.
(English)
[J] Int. J. Numer. Methods Fluids 66, No. 12, 1506-1529 (2011). ISSN 0271-2091; ISSN 1097-0363/e

The authors consider a diffusion-reaction parabolic equation in $d$ ($\le 3$) dimensions and continue their development of dynamic parallel Galerkin domain decomposition methods based on the work of {\it C. N. Dawson} and {\it T. F. Dupont} [Math. Comput. 58, No.~197, 21--34 (1992; Zbl 0746.65072)] and the former work by {\it K. Ma, T. Sun} and {\it 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.
[Gisbert Stoyan (Budapest)]
MSC 2000:
*65M60 Finite numerical methods (IVP of PDE)
65M55 Multigrid methods; domain decomposition (IVP of PDE)
35K57 Reaction-diffusion equations
65Y05 Parallel computation (numerical methods)
65M50 Mesh generation and refinement (IVP of PDE)

Keywords: diffusion-reaction parabolic equation; domain decomposition; Galerkin method; inter-domain boundary flux calculation; error estimates; parallel computation; finite element; numerical experiments; grid modification; integral mean method

Citations: Zbl 0746.65072; Zbl 1173.65061

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