A SCATTERED DATA INTERPOLANT FOR THE SOLUTION OF THREE-DIMENSIONAL PDES

Using a Difierential Equation Interpolant (DEI), one can accurately approx- imate the solution of a Partial Difierential Equation (PDE) at ofi-mesh points. The idea is to allocate a multi-variate polynomial to each mesh element and consequently, the collection of such polynomials over all mesh elements will deflne a piecewise polynomial approximation. In this paper we will investigate such interpolants on a three-dimensional unstructured mesh. As reported in (1), for a tetrahedron mesh in three dimensions, tensor product tri-quadratic and pure tri-cubic interpolants are the most appropriate candidates. We will report on the efiectiveness of these alternatives on some typical PDEs.