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Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

Published online by Cambridge University Press:  20 August 2015

M. J. Baines ,
M. E. Hubbard  and
P. K. Jimack
M. J. Baines*
Affiliation:
Department of Mathematics, The University of Reading, RG6 6AX, UK
M. E. Hubbard*
Affiliation:
School of Computing, University of Leeds, LS2 9JT, UK
P. K. Jimack*
Affiliation:
School of Computing, University of Leeds, LS2 9JT, UK
*
Corresponding author.Email:m.j.baines@reading.ac.uk
Email:m.e.hubbard@leeds.ac.uk
Email:p.k.jimack@leeds.ac.uk

Abstract

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This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Keywords

35R3565M6076M10Time-dependent nonlinear diffusionmoving boundariesfinite element methodLagrangian meshesconservation of mass

Information

Type
Review Article
Information
Communications in Computational Physics , Volume 10 , Issue 3 , September 2011 , pp. 509 - 576
Copyright
Copyright © Global Science Press Limited 2011

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