TY - JOUR T1 - A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 40 EP - 52 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2009.m9002 UR - https://global-sci.org/intro/article_detail/nmtma/5988.html KW - Legendre spectral Galerkin method, two-point boundary value problem, superconvergence, a-posteriori error estimation AB -

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.