*Pacific Northwest Numerical Analysis Seminar*

October 9, 1999

*A Moving Mesh Method for Higher Dimensional PDEs*

Robert D. Russell

We will discuss an adaptive grid method based upon a moving mesh
approach for solving time dependent PDEs. The approach is based
upon a moving mesh PDE (MMPDE) formulation. In higher dimensions,
the MMPDE is derived from a heat flow equation which arises using a
mesh adaptation functional in turn motivated from the theory of
harmonic maps. Geometrical interpretations are given for the heat
equation and functional, and basic properties of this MMPDE are
discussed.

The method is relatively simple and easy to program. Numerical
examples are presented where it is used both for mesh generation and
for solving time dependent parabolic PDEs. The results demonstrate
the potential of the mesh movement strategy to concentrate the mesh
points so as to adapt to special problem features and to also preserve
a suitable level of mesh smoothness (usually measured by the mesh
orthogonality).

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