C1 continuous solutions from the Green element method using Overhauser elements

The Green element method (GEM) is an element-by-element approach to the boundary element method. It generates large sparse coefficient matrices (in the same manner that the finite element method would) while still exploiting the useful properties of Green's functions. GEM has been applied to a variety of problems including aquifer flows, contaminant transport, and petroleum reservoir engineering. In many engineering problems C1 continuity of the computed solution is desirable, for example when deriving flow velocities from pressures computed from a partial differential equation describing flow in porous media. The developers of GEM have given the issue of C1 continuity some attention by deriving a form of GEM which uses Hermitian elements. This paper presents an alternative approach to C1 continuity which is based on Overhauser elements. Unlike Hermitian elements these elements interpolate the unknown over the element in terms of the nodal values of the unknown only, and do not work in terms of spatial derivatives of the unknown.