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Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations
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Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 3 : pp. 509–576

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.201010.040511a

Communications in Computational Physics, Vol. 10 (2011), Iss. 3 : pp. 509–576

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    68

Keywords:   

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