Journal de mathématiques appliquées et computationnelles

Verification of Numerical Solutions of the Advection-Diffusion and Burgers Equations

Abstract

Carlos Henrique Marchi and Arileide Cristina Alves

The purpose of this work is to verify the asymptotic order of the discretization error of two one-dimensional problems modeled by the advection-diffusion and Burgers equations. The problems are solved using first and second-order accurate spatial approximations, with and without mixing (hybrid scheme), by deferred correction. It was verified that the accuracy of hybrid schemes is equal to that of the lowest-order pure scheme.