抄録
The purpose of this paper is to present an attempt at a numerical treat ment of a kind ofunder-determined problem of the Laplace equation in two spatial dimensions. A resolutionis sought for the problem in which the Dirichlet and Neumann data are arbitrarily imposedon each part of the boundary of the domain. This new problem can be regarded as aboundary inverse problem, in which the proper boundary conditions are to be identified for the rest of the boundary. The solution of this problem is not unique. The treat mentis based on the direct variational method, and a functional is minimized by the method of the steepest descent. The minimization problem is recast into successive primary anddual boundary value problems of the Laplace equation. After numerical computations byusing the boundary elements, it is concluded that our scheme is stable, but the numericalsolutions converge to the nearest local minimum.
