On a Robin-Robin domain decomposition method with optimal convergence rate

Details On a Robin-Robin domain decomposition method with optimal convergence rate On a Robin-Robin domain decomposition method with optimal convergence rate

2011-12-19

arxiv.org/abs/1112.4327v1

Mathematics

Numerical Analysis

Scientific paper

In this paper, we shall solve a long-standing open problem: Is it possible that the convergence rate of the Lions' Robin-Robin nonoverlapping domain decomposition(DD) method is independent of the mesh size $h$? We shall design a two-parameter Robin-Robin domain decomposition method. It is shown that the new DD method is optimal, which means the convergence rate is independent of the mesh size $h$. The traditional Robin-Robin domain decomposition method converges at a rate of $1-O(h^{1/2})$, even under the optimal parameter. Numerical implementation confirming our theoretical findings shall be given.

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