Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

M. J. Baines, M. E. Hubbard, P. K. Jimack
2011 Communications in Computational Physics  
AbstractThis 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
more » ... ltidimensional 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.
doi:10.4208/cicp.201010.040511a fatcat:734zz53wvvbgxa3bau6ufy5kfy