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

摘要

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.!8