On the solution of elliptic partial differential equations on regions with corners

JOURNAL OF COMPUTATIONAL PHYSICS

卷:305

Article

Serkh, Kirill¹  Rokhlin, Vladimir¹ 

[1] Yale Univ, Dept Math, New Haven, CT 06511 USA

关键词: Boundary value problems;    Potential theory;    Corners;    Singular solutions;    Elliptic partial differential equations;   

DOI  :  10.1016/j.jcp.2015.10.024

来源: Elsevier

【 摘 要 】

In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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