High-order interpolation methods for finite-element solved potential distributions in the two-dimensional rectilinear coordinate system

Abstract

This paper compares the accuracy of three high order interpolation methods to drive spatial derivative information from finite element meshes in the 2D rectilinear coordinate system. These methods involve using a C 1 triangle interpolant, spline/hermite cubic interpolation, and a local polynomial function fit. 2D electric potential distributions are analyzed for a test example on which the radial electric field is evaluated at scattered points in a domain composed of block regions. The results show that of the methods considered, a local polynomial expansion suing basis functions which satisfy Laplace's equation is the most accurate. The better accuracy of this method however, can only be obtained for potential distributions that have a low degree of discretization noise at their mesh nodes.