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

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

DOI: 10.4208/cicp.201010.040511a

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

Published online: 2011-10

[An open-access article; the PDF is free to any online user.]

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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.

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@Article{CiCP-10-509, author = {M. J. Baines, M. E. Hubbard and P. K. Jimack}, title = {Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.201010.040511a}, url = {http://global-sci.org/intro/article_detail/cicp/7452.html} }
TY - JOUR T1 - Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations AU - M. J. Baines, M. E. Hubbard & P. K. Jimack JO - Communications in Computational Physics VL - 3 SP - 509 EP - 576 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.201010.040511a UR - https://global-sci.org/intro/article_detail/cicp/7452.html KW - AB -

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.

M. J. Baines, M. E. Hubbard and P. K. Jimack. (2011). Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations. Communications in Computational Physics. 10 (3). 509-576. doi:10.4208/cicp.201010.040511a
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