@Article{IJNAM-16-575, author = {Guo , RuchiLin , Tao and Zhuang , Qiao}, title = {Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {4}, pages = {575--589}, abstract = {

This paper is for proving that the partially penalized immersed finite element (PPIFE) methods developed in [25] converge optimally under the standard piecewise $H$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 $H$regularity was assumed. Furthermore, with the standard piecewise $H$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 $H$regularity requirement.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13015.html} }