On the Stability of Boundary Element Methods for Integral Equations of the First Kind

Abstract

A larger class of two-dimensional elliptic boundary value problems in elasticity and fluid mechanics can be reduced to systems of boundary integral equations of the first kind. This paper is concerned with the stability analysis of boundary element methods for treating such a class of integral equations. In particular, the problem of ill-posedness, the optimal rate of convergence, and its connection with Tikhonov regularization procedure will be discussed.