Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations (Communications in Computational Physics, 2011)
This article describes a number of velocity-based moving mesh numericalmethods for multidimensional nonlinear time-dependent partial differential equations(PDEs). It consists of a short historical review followed by a detailed description of arecently developed multidimensional moving mesh finite element method based onconservation. Finite element algorithms are derived for both mass-conserving andnon mass-conserving problems, and results shown for a number of multidimensionalnonlinear test problems, including the second order porous medium equation and thefourth order thin film equation as well as a two-phase problem. Further applicationsand extensions are referenced.