@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.201010.040511a},
url = {http://global-sci.org/intro/article_detail/cicp/7452.html}
}