A Spectral Difference Method with Dubiner Polynomials on Triangulations

摘要

This current work focusses on developing a Spectral Difference Method using Dubiner expansion instead of Lagrange interpolation. The Dubiner basis is introduced and modifications occurring in the update scheme are presented. Furthermore, attention is paid to possible distributions for the flux points on a standard triangle. First numerical tests for the linear advection equation show convergence and the need for stabilization for high orders.