1. Convergence of a FEM and two-grid algorithms for elliptic problems on disjoint domains
- Author
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Jovanovic, Boško S., Koleva, Miglena N., and Vulkov, Lubin G.
- Subjects
- *
STOCHASTIC convergence , *FINITE element method , *ALGORITHMS , *MATHEMATICAL decoupling , *NUMERICAL analysis , *RECTANGLES , *PROBLEM solving - Abstract
Abstract: In this paper, we analyze a FEM and two-grid FEM decoupling algorithms for elliptic problems on disjoint domains. First, we study the rate of convergence of the FEM and, in particular, we obtain a superconvergence result. Then with proposed algorithms, the solution of the multi-component domain problem (simple example — two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms. [Copyright &y& Elsevier]
- Published
- 2011
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