Superconvergence of partially penalized immersed finite element methods

Abstract

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..