In general, a physical problem governed by a linear elliptic partial differential equation but with a shell discontinuity in the domain cannot be efficiently solved using the traditional boundary element method. This paper shows how the Laplace equation can be solved in an interior region containing shell discontinuities by recasting it as an integral equation known as a boundary and shell integral equation and applying colloction to derive a method termed the boundary and shell element method. Direct and indirect methods are derived and applied to a test problem.

Shell elements for Laplace problems are available in the author's package BEMLAP package.