TY - JOUR
T1 - Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh
AU - Hailong Guo & Xu Yang
JO - Communications in Computational Physics
VL - 5
SP - 1488
EP - 1511
PY - 2018
DA - 2018/08
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2017-0026
UR - https://global-sci.org/intro/article_detail/cicp/12630.html
KW - Elliptic interface problem, gradient recovery, superconvergence, body-fitted mesh, a posteriori error estimator, adaptive method.
AB - <p style="text-align: justify;">In this paper, we propose a new gradient recovery method for elliptic interface
problem using body-fitted meshes. Due to the lack of regularity of the solution at
the interface, standard gradient recovery methods fail to give superconvergent results
and thus will lead to overrefinement when served as <span style="font-family: ">a posteriori</span> error estimators. This
drawback is overcome by designing a new gradient recovery operator. We prove the
superconvergence of the new method on both mildly unstructured meshes and adaptive
meshes. Several numerical examples are presented to verify the superconvergence
and its robustness as <span style="font-family: ">a posteriori</span> error estimator.</p>