@Article{CiCP-10-509, author = {}, 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} }