The collocation method for mixed boundary value problems on domains with curved polygonal boundaries

被引：0
|
作者：
J. Elschner
Y. Jeon
I.H. Sloan
E.P. Stephan
机构：
[1] Weierstraß–Institut für Angewandte Analysis und Stochastik,
[2] Mohrenstr. 39,undefined
[3] D–10117 Berlin,undefined
[4] Germany,undefined
[5] Department of Mathematics,undefined
[6] Ajou University,undefined
[7] Suwon 441–749,undefined
[8] Korea,undefined
[9] School of Mathematics,undefined
[10] University of New South Wales,undefined
[11] Sydney 2062,undefined
[12] Australia,undefined
[13] Institut für Angewandte Mathematik,undefined
[14] Universität Hannover,undefined
[15] Postfach 6009,undefined
[16] D-30060 Hannover,undefined
[17] Germany,undefined
来源：
Numerische Mathematik | 1997年 / 76卷
关键词：
Key words: trigonometric collocation method, mixed boundary value problem for the Laplacian, polygonal domains Mathematics Subject Classification (1991): 65 N 38, 65 N 35, 65 R 20;
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学科分类号：
摘要：
We consider an indirect boundary integral equation formulation for the mixed Dirichlet-Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and a cosine approximating space. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. A complete stability and solvability analysis of the transformed integral equations is given by use of a Mellin transform technique, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space.
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页码：355 / 381
页数：26
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