@Article{JCM-40-5,
author = {Wang, Kai and Wang, Na},
title = {Analysis of a Fully Discrete Finite Element Method for Parabolic Interface Problems with Nonsmooth Initial Data},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {5},
pages = {777--793},
abstract = {<p style="text-align: justify;">This article concerns numerical approximation of a parabolic interface problem with general $L^2$ initial value. The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface, with piecewise linear approximation to the interface. The semi-discrete finite element problem is furthermore discretized in time by the $k$-step backward difference formula&nbsp; with $ k=1,\ldots,6 $. To maintain high-order convergence in time for possibly nonsmooth $L^2$ initial value, we modify the standard backward difference formula at the first $k-1$ time levels by using a method recently developed for fractional evolution equations. An error bound of $\mathcal{O}(t_n^{-k}\tau^k+t_n^{-1}h^2|\log h|)$ is established for the fully discrete finite element method for general $L^2$ initial data.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2101-m2020-0075},
url = {https://global-sci.com/article/84202/analysis-of-a-fully-discrete-finite-element-method-for-parabolic-interface-problems-with-nonsmooth-initial-data}
}