Velocity-based moving mesh methods for nonlinear partial differential equations

Baines, M. J., Hubbard, M. E. and Jimack, P. K. (2011) Velocity-based moving mesh methods for nonlinear partial differential equations. Communications in Computational Physics, 10 (3). pp. 509-576. ISSN 1991-7120 doi: 10.4208/cicp.201010.040511a

Abstract/Summary

This article describes a number of velocity-based moving mesh numerical methods formultidimensional 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.