TY - JOUR
T1 - Superconvergence Analysis of the Polynomial Preserving Recovery for Elliptic Problems with Robin Boundary Conditions
AU - Du , Yu
AU - Wu , Haijun
AU - Zhang , Zhimin
JO - Journal of Computational Mathematics
VL - 1
SP - 223
EP - 238
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1911-m2018-0176
UR - https://global-sci.org/intro/article_detail/jcm/13692.html
KW - Superconvergence, Polynomial preserving recovery, Finite element methods, Robin boundary condition.
AB - <p style="text-align: justify;">We analyze the superconvergence property of the linear finite element method based on the polynomial preserving recovery (PPR) for Robin boundary elliptic problems on triangulations. First, we improve the convergence rate between the finite element solution and the linear interpolation under the $H^1$-norm by introducing a class of meshes satisfying the $Condition$ $(\alpha,\sigma,\mu)$. Then we prove the superconvergence of the recovered gradients post-processed by PPR and define an asymptotically exact a posteriori error estimator. Finally, numerical tests are provided to verify the theoretical findings.</p>