Practical Error Estimation for Discretized Models

Imagine the following situation: your boss asks you to get a measure of reliability and convergence speed for some new software that solves an important problem. Your company has spent a lot of money on it and the modules of the code consist of many thousands of lines. The documentation accompanying the code emphasizes its superiority and shows a lot of impressive figures, but says little about its reliability and accuracy. You should make your own experiments, solving a given task several times, changing the problem data and numerical parameters for each experiment, and analyzing the outcomes. Try to get estimates of the error even if-except in trivial cases-the exact solution is not known. The present chapter provides some guidance to help you with this.