Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations
M. J. Baines 1*, M. E. Hubbard 2, P. K. Jimack 21 Department of Mathematics, The University of Reading, RG6 6AX, UK.
2 School of Computing, University of Leeds, LS2 9JT, UK.
Received 20 October 2010; Accepted (in revised version) 4 May 2011
Available online 1 June 2011
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.AMS subject classifications: 35R35, 65M60, 76M10
Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Time-dependent nonlinear diffusion, moving boundaries, finite element method, Lagrangian meshes, conservation of mass.
Email: firstname.lastname@example.org (M. Baines), email@example.com (M. E. Hubbard), firstname.lastname@example.org (P. K. Jimack)