A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension

Abstract

In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for  two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postprocess improves the order of convergence. Consequently, we obtain asymptotically exact a-posteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.