TY - JOUR
T1 - Uniform Superconvergence of Galerkin Methods for Singularly Perturbed Problems
JO - Journal of Computational Mathematics
VL - 2
SP - 273
EP - 288
PY - 2010
DA - 2010/04
SN - 28
DO - http://doi.org/10.4208/jcm.2009.10-m2870
UR - https://global-sci.org/intro/article_detail/jcm/8519.html
KW - singularly perturbed, Hermite splines, Shishkin-type meshes, Interpolation post-processing, Uniform superconvergence.
AB - <p style="text-align: justify;">In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper.</p>