Vol. 123, No. 2 * Pages 135–264 * April - June 2019

Richardson extrapolation is a numerical procedure which enables us to enhance the accuracy of any convergent numerical method in a simple and powerful way.
In this paper we overview the theoretical background of Richardson extrapolation in space and time, where two numerical solutions, obtained on a coarse and a fine space-time grid are combined by a suitable weighted average. We show that when the Crank-Nicolson method is appropriately combined with this extrapolation technique for the solution of the one-dimensional advection equation, then the order of accuracy increases by two both in time and space. The theoretically derived consistency order and the necessity of the smoothness conditions for the exact solution and for the advection velocity are illustrated by numerical experiments, performed by the advection module of the Danish Eulerian Model (DEM).