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Moving mesh methods for solving time dependent PDEs
R D Russell (Invited Presentation)
Department of Mathematics and Statistics,
Simon-Fraser University,
Burnaby, British Columbia,
V5A 1S6, Canada
Abstract
We will discuss the class of adaptive grid meth
ods often called moving
mesh methods (or dynamic methods - in contrast to the static methods).
We shall briefly review these methods and present the approach of using
MMPDEs (moving mesh PDEs) for smoothly adapting the meshes in time. The
various versions can be seen to be not only simple and relatively easy to
program, but a fairly complete mathematical analysis of the properties of
the MMPDEs with smoothing has been carried out for 1D (one spatial
dimension). Software developed using this approach for solving 1D
problems is illustrated for some physical problems displaying a variety
of different solution behaviours, including some blowup problems in
combustion theory. We discuss recent progress (joint work with W. Huang)
in extending these developments to higher dimensions. The mesh must now
adapt to the special problem features while preserving a suitable level
of smoothness (usually measured by the mesh orthogonality).
Last modified Fri Jun 21 19:19:15 GB-Eire 1996
(DBD)