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

作者：Yi, Lijun; Guo, Benqi^*

来源：Numerical Mathematics: Theory, Methods and Applications , 2010, 3(1): 40-52.

DOI：10.4208/nmtma.2009.m9002

• Legendre spectral Galerkin method
• two-point boundary value problem
• superconvergence
• a-posteriori error estimation

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.

• 出版日期2010-2
• 单位上海师范大学