Preprint 2001-039

A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions

R. Li, T. Tang, and P.-W. Zhang


Abstract: A framework for adaptive meshes based on the Hamilton-Schoen-Yau theory was proposed by Dvinsky. In a recent work [J. Comput. Phys. 170, 562-588 (2001)], we extended Dvinsky's method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability. In this work, we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions. In obtaining the variational mesh, we will solve an {\em optimization problem} with some appropriate constraints, which is in contrast to the traditional method of solving the Euler-Lagrange equation directly. The key idea of this approach is to update the interior and boundary grids simultaneously, rather than considering them separately. Application of the proposed moving mesh scheme is illustrated with some two- and three-dimensional problems with large solution gradients. The numerical experiments show that our methods can accurately resolve detailed features of singular problems in 3D.


Paper:
Available as PostScript (5.5 Mbytes) or gzipped PostScript (1.2 Mbytes; uncompress using gunzip).
Author(s):
R. Li, <rli@math.hkbu.edu.hk>
T. Tang , <ttang@math.hkbu.edu.hk>
P.-W. Zhang, <pzhang@math.pku.edu.cn>
Publishing information:
Comments:
Submitted by:
<ttang@math.hkbu.edu.hk> October 5 2001.


[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <conservation@math.ntnu.no>
Last modified: Mon Oct 8 09:14:36 MET DST 2001