A method of lines based on immersed finite elements for parabolicmoving interface problems

Tao Lin, Yanping Lin, Xu Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

31 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)548-568
Number of pages21
JournalAdvances in Applied Mathematics and Mechanics
Volume5
Issue number4
DOIs
Publication statusPublished - 27 Jun 2013

Keywords

  • Cartesian mesh
  • Immersed finite element
  • Method of lines
  • Moving interface

ASJC Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics

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