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A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems

Published online by Cambridge University Press:  03 June 2015

Tao Lin ,
Yanping Lin  and
Xu Zhang
Tao Lin*
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
Yanping Lin*
Affiliation:
Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong Department of Mathematical and Statistics Science, University of Alberta, Edmonton AB, T6G 2G1, Canada
Xu Zhang*
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
*
Email: tlin@math.vt.edu
Corresponding author. Email: malin@polyu.edu.hk
Email: xuz@vt.edu
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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 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.

Keywords

35R0565M2065M60Immersed finite elementmoving interfacemethod of linesCartesian mesh
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Special Issue 4 , August 2013 , pp. 548 - 568
Copyright
Copyright © Global-Science Press 2013

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