Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/12893
Title: A method of lines based on immersed finite elements for parabolicmoving interface problems
Authors: Lin, T
Lin, Y 
Zhang, X
Keywords: Cartesian mesh
Immersed finite element
Method of lines
Moving interface
Issue Date: 2013
Publisher: Global Science Press
Source: Advances in Applied Mathematics and Mechanics, 2013, v. 5, no. 4, p. 548-568 How to cite?
Journal: Advances in Applied Mathematics and Mechanics 
Abstract: 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 fixedmesh (such as a Cartesianmesh if desired), and this featuremakes 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.
URI: http://hdl.handle.net/10397/12893
ISSN: 2070-0733
DOI: 10.4208/aamm.13-13S11
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