On the convergence of a space decomposition method (Q2702877)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the convergence of a space decomposition method |
scientific article |
Statements
7 October 2001
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minimizer problem
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space decomposition
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domain decomposition
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geometrical convergence
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asymptotic convergence rate
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On the convergence of a space decomposition method (English)
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In this short paper the authors discuss the numerical approximation of the minimizer problem \(F(u)=\min_{v\in V} F(v)\), where \(F(v)\) is a functional defined on the space \(V\). Using a space decomposition and the domain decomposition method, the authors prove two geometrical convergence theorems of the space decomposition method under the condition that \(F\) is twice continuously differentiable. The result of this paper weakens the condition upon \(F\) in the work of \textit{X.-C. Tai} and \textit{M. Espedal} [SIAM J. Numer. Anal. 35, 1558-1570 (1998; Zbl 0915.65063)] where \(f\) is assumed in \(C^3\).
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