TY - JOUR T1 - Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems AU - Guo , Ruchi AU - Lin , Tao AU - Zhuang , Qiao JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 575 EP - 589 PY - 2019 DA - 2019/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13015.html KW - Interface problems, immersed finite element methods, optimal convergence, discontinuous coefficients, finite element spaces, interface independent mesh, regularity. AB -

This paper is for proving that the partially penalized immersed finite element (PPIFE) methods developed in [25] converge optimally under the standard piecewise $H$2 regularity assumption for the exact solution. In energy norms, the error estimates given in this paper are better than those in [25] where a stronger piecewise $H$3 regularity was assumed. Furthermore, with the standard piecewise $H$2 regularity assumption, this paper proves that these PPIFE methods also converge optimally in the $L$2 norm which could not be proved in [25] because of the excessive $H$3 regularity requirement.