@Article{IJNAM-10-298,
author = {T. Lin and D. Sheen},
title = {The Immersed Finite Element Method for Parabolic Problems Using the Laplace Transformation in Time Discretization},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {2},
pages = {298--313},
abstract = {<p style="text-align: justify;">In this paper we are interested in solving parabolic problems with a piecewise constant
diffusion coefficient on structured Cartesian meshes. The aim of this paper is to investigate the
applicability and convergence behavior of combining two non-conventional but innovative methods:
the Laplace transformation method in the discretization of the time variable and the immerse finite
element method (IFEM) in the discretization of the space variable. The Laplace transformation
in time leads to a set of Helmholtz-like problems independent of each other, which can be solved
in highly parallel. The employment of immerse finite elements (IFEs) makes it possible to use
a structured mesh, such as a simple Cartesian mesh, for the discretization of the space variable
even if the material interface (across which the diffusion coefficient is discontinuous) is non-trivial.
Numerical examples presented indicate that the combination of these two methods can perform
optimally from the point of view of the degrees of polynomial spaces employed in the IFE spaces.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/569.html}
}