Superconvergence of partially penalized immersed finite element methods
Hailong Guo, Xu Yang, Zhimin Zhang
IMA JOURNAL OF NUMERICAL ANALYSIS | OXFORD UNIV PRESS | Published : 2018
The contribution of this article contains two parts: first, we prove a supercloseness result for the partially penalized immersed finite element (PPIFE) methods in (Lin, T., Lin, Y. & Zhang, X. (2015), Partially penalized immersed finite element methods for elliptic interface problems. SIAM J. Numer. Anal., 53, 1121-1144) and then based on the supercloseness result, we show that the gradient recovery method proposed in our previous work (Guo, H. & Yang, X. (2017) Gradient recovery for elliptic interface problem: II. Immersed finite element methods. J. Comput. Phys., 338, 606-619) can be applied to the PPIFE methods and the recovered gradient converges to the exact gradient with a superconver..View full abstract
Awarded by U.S. National Science Foundation
Awarded by National Natural Science Foundation of China
U.S. National Science Foundation grants (DMS-1418936 to X.Y., DMS-1419040 to Z.Z.); Hellman Family Foundation Fellowship, University of California, Santa Barbara; and the National Natural Science Foundation of China grants (NSFC 11471031, NSFC 91430216, and NASF U1530401).