A Posteriori Error Estimate for the 1D Wave Equation

The error of numerical schemes in heterogeneous media is difficult to analyse. In this paper, we derive an a posteriori estimate for the unidimensional wave equation in heterogeneous media. This estimate can be used as a tool to measure the precision of the numerical schemes in such media. The main result is based on a fundamental lemma given by Babuska and Rheinboldt for elliptic problems. We use this result to drive an error estimate for the semi-discrete problem. We also derive an estimate for the fully discretized problem