摘要
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.
