TY - JOUR T1 - Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations 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.