Estimation of the Distance between True and Numerical Solutions

Abstract

Given an ensemble of numerical solutions generated by different algorithms that are guaranteed to have different errors, the triangle inequality is used to find a neighborhood of a numerical solution that contains the true one. By analyzing the distances between the numerical solutions, the latter can be ranged according to their error magnitudes. Numerical tests for the two-dimensional compressible Euler equations demonstrate the possibility of comparing the errors of different methods and determining a domain containing the true solution.