New Scheme for the Approximation of Advection-Diffusion Equations by Collocation

摘要

A competitive algorithm, which allows the computation of approximated polynomialsolutions of advection-diffusion equations in the square, is presented. The equation is collocated at a special grid and the corresponding system is solved by a low-cost preconditioned iterative procedure. The method provides accurate results even when the solution presents sharp boundary-layers.