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Volume 5, Issue 4
A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems

Tao Lin, Yanping Lin & Xu Zhang

Adv. Appl. Math. Mech., 5 (2013), pp. 548-568.

Published online: 2013-08

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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

Immersed finite element, moving interface, method of lines, Cartesian mesh.

  • AMS Subject Headings

35R05, 65M20, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-548, author = {Tao and Lin and and 20110 and and Tao Lin and Yanping and Lin and and 20111 and and Yanping Lin and Xu and Zhang and and 20112 and and Xu Zhang}, 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 = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.13-13S11}, url = {http://global-sci.org/intro/article_detail/aamm/85.html} }
TY - JOUR T1 - A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems AU - Lin , Tao AU - Lin , Yanping AU - Zhang , Xu JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 548 EP - 568 PY - 2013 DA - 2013/08 SN - 5 DO - http://doi.org/10.4208/aamm.13-13S11 UR - https://global-sci.org/intro/article_detail/aamm/85.html KW - Immersed finite element, moving interface, method of lines, Cartesian mesh. AB -

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.

Tao Lin, Yanping Lin & Xu Zhang. (1970). A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems. Advances in Applied Mathematics and Mechanics. 5 (4). 548-568. doi:10.4208/aamm.13-13S11
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