@Article{AAMM-5-4,
author = {Tao, Lin and Yanping, Lin and Zhang, Xu},
title = {A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2013},
volume = {5},
number = {4},
pages = {548--568},
abstract = {<p style="text-align: justify;">This article extends the finite element method of lines to a parabolic
initial boundary value problem whose diffusion coefficient is discontinuous
across an interface that changes with respect to time. The method presented
here uses immersed finite element (IFE) functions for the discretization in
spatial variables that can be carried out over a fixed mesh (such as a
Cartesian mesh if desired), and this feature makes it possible to reduce
the parabolic equation to a system of ordinary differential equations (ODE)
through the usual semi-discretization procedure. Therefore, with a suitable
choice of the ODE solver, this method can reliably and efficiently solve a
parabolic moving interface problem over a fixed structured (Cartesian) mesh.
Numerical examples are presented to demonstrate features of this new method.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.13-13S11},
url = {https://global-sci.com/article/73506/a-method-of-lines-based-on-immersed-finite-elements-for-parabolic-moving-interface-problems}
}