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 - <p style="text-align: justify;">In this paper, a-posteriori error estimators are proposed for the
Legendre spectral Galerkin method for &nbsp;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.</p>