Optimal order collocation for the mixed boundary value problem on polygons (Q2701554)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal order collocation for the mixed boundary value problem on polygons |
scientific article |
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Optimal order collocation for the mixed boundary value problem on polygons (English)
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19 February 2001
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numerical examples
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mixed Dirichlet-Neumann problem
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polygonal domain
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splines
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optimal order
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error bounds
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stability
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Fix collocation method
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The author builds collocation methods based on a mixed single and double layer potential for the mixed Dirichlet-Neumann problem in a plane polygonal domain. The boundary values of this potential define a bijective boundary operator if a modified capacity adapted to the problem is not 1. The author construct an optimal order Fix collocation method without mesh grading and with full numerically stability. It is based on smoothest splines. If splines of order \(2m-1\) are used, the quasi-optimal estimates are obtained in \(H^m\)-norm. The efficiency of the methods are demonstrated by some numerical computations.
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