On a Robin-robin Domain Decomposition Method with Optimal Convergence Rate
نویسندگان
چکیده
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(h1/2), even under the optimal parameter. Numerical implementation confirming our theoretical findings shall be given. AMS subject classifications. Primary 65N30; Secondary 65M60
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تاریخ انتشار 2011