@Article{IJNAM-16-4,
author = {Ruchi, Guo and Tao, Lin 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 = {<p style="text-align: justify;">This paper is for proving that the partially penalized immersed finite element (PPIFE)
methods developed in [25] converge optimally under the standard piecewise $H$<sup>2&nbsp;</sup>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 $H$<sup>3&nbsp;</sup>regularity was assumed. Furthermore, with the
standard piecewise $H$<sup>2&nbsp;</sup>regularity assumption, this paper proves that these PPIFE methods also
converge optimally in the $L$<sup>2</sup> norm which could not be proved in [25] because of the excessive $H$<sup>3&nbsp;</sup>regularity requirement.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-13015},
url = {https://global-sci.com/article/83077/improved-error-estimation-for-the-partially-penalized-immersed-finite-element-methods-for-elliptic-interface-problems}
}