TY - JOUR
T1 - Recovery-Based a Posteriori Error Estimation for Elliptic Interface Problems Based on Partially Penalized Immersed Finite Element Methods
AU - Chen , Yanping
AU - Deng , Zhirou
AU - Huang , Yunqing
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 126
EP - 155
PY - 2022
DA - 2022/03
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/20352.html
KW - Interface problems, a posteriori error estimation, immersed finite element methods, gradient recovery, adaptive algorithm.
AB - <p style="text-align: justify;">This paper develops a recovery-based a posteriori error estimation for elliptic interface problems based on partially penalized immersed finite element (PPIFE) methods. Due to the low regularity of solution at the interface, standard gradient recovery methods cannot obtain superconvergent results. To overcome this drawback a new gradient recovery method is proposed that applies superconvergent cluster recovery (SCR) operator on each subdomain and weighted average (WA) operator at recovering points on the approximated interface. We prove that the recovered gradient superconverges to the exact gradient at the rate of $O(h^{1.5}).$ Consequently, the proposed method gives an asymptotically exact a posteriori error estimator for the PPIFE methods and the adaptive algorithm. Numerical examples show that the error estimator and the corresponding adaptive algorithm are both reliable and efficient.</p>