Volume 10, Issue 3
Velocity-based Moving Mesh Methods for Nonlinear Partial Differential Equations

M. J. Baines ,  M. E. Hubbard and P. K. Jimack

10.4208/cicp.201010.040511a

Commun. Comput. Phys., 10 (2011), pp. 509-576.

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  • Abstract

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.

  • History

Published online: 2011-10

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