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 - <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>