TY - JOUR
T1 - Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities
JO - Journal of Computational Mathematics
VL - 1
SP - 11
EP - 31
PY - 2010
DA - 2010/02
SN - 28
DO - http://doi.org/10.4208/jcm.2009.09-m1002
UR - https://global-sci.org/intro/article_detail/jcm/8504.html
KW - Superconvergence, Graded meshes, Weighted Sobolev spaces, Singular solutions, The finite element method, Gradient recovery schemes.
AB - <p style="text-align: justify;">For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the $L^2$-projection from the piecewise constant field $∇u_N$ to the continuous and piecewise linear finite element space gives a better approximation of $∇u$ in the $H^1$-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.</p>