Optimal error bounds for partially penalized immersed finite element methods for parabolic interface problems

Abstract In Lin et al. (2015), a group of typical partially penalized immersed finite element (PPIFE) methods were developed for solving interface problems of the parabolic equations, and its authors proved that these PPIFE methods had the optimal O ( h ) convergence rate in an energy norm under a sub-optimal piecewise H 3 regularity assumption. In this article, we report our reanalysis of these PPIFE methods. Our proofs are based on the optimal error bounds recently derived in Guo et al. (2019) for elliptic interface problems, and we are able to show that these PPIFE methods have the optimal convergence not only in an energy norm but also in the usual L 2 norm with the assumption that the exact solution possesses the standard piecewise H 2 regularity instead of the excessive piecewise H 3 regularity in the space variable. Numerical results are also presented to validate the reported error analysis.