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

A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems
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Year:    2013

Author:    Tao Lin, Yanping Lin, Xu Zhang

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 548–568

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.13-13S11

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 548–568

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Immersed finite element moving interface method of lines Cartesian mesh.

Author Details

Tao Lin

Yanping Lin

Xu Zhang

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