WIT Press


Direct Method Of Solution For General Boundary Value Problem Of The Laplace Equation

Price

Free (open access)

Paper DOI

10.2495/BE000201

Volume

26

Pages

8

Published

2000

Size

448 kb

Author(s)

K. Onishi & Y. Ohura

Abstract

Two-dimensional Laplace equation is considered in the domian enclosed by a smooth curve. The Dirichlet data are prescribed on a part of the bound- ary, while the Neumann data are prescribed on a part of the boundary. This problem is reformulated in terms of the variational problem, which is then recast into primary and dual boundary value problems of the Laplace equation. A direct method of solution using the BEM is presented. This proposes a unified treatment of conventional boundary value problem, the Cauchy problem, and under- or over-determined problems. 1 Introduction Let £1 be a simply connected bounded domain with its smooth boundary F in JR^ Let n be the exterior normal to the boundary. We consider the Laplace equation;

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