The boundary element method for linear partial differential equations with variable coefficients (Q1893932)

The effectiveness of the boundary element method for the solution of a wide class of problems for elliptic equations with constant coefficients is now well established. In contrast, the method has not been widely used to solve problems governed by linear elliptic equations with variable coefficients. For such equations it is often possible to obtain the relevant integral equation together with a formal expression for its kernel incorporating the relevant fundamental solution or Green's function. The purpose of this paper is to outline some cases when the fundamental solution is in a relatively simple form and in such cases the boundary element method does provide an effective procedure for the numerical solution of problems involving equations with variable coefficients.