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Analysis of moving mesh partial differential equations with spatial smoothing
Huang, Weizhang Russell, Robert D.
Huang, Weizhang
Russell, Robert D.
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Abstract
Two moving mesh partial differential equations (MMPDEs) with spatial smoothing are derived based upon the equidistribution principle. This smoothing technique is motivated by the robust moving mesh method of Dorfi and Drury [J. Comput. Phys., 69 (1987), pp. 175--195]. It is shown that under weak conditions the basic property of no node-crossing is preserved by the spatial smoothing, and a local quasi-uniformity property of the coordinate transformations determined by these MMPDEs is proven. It is also shown that, discretizing the MMPDEs using centered finite differences, these basic properties are preserved.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/S0036142993256441.
Date
1997-06-01
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Society for Industrial and Applied Mathematics
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Keywords
moving mesh PDE, spatial smoothing
Citation
Huang, Weizhang & Russell, Robert D. "Analysis of moving mesh partial differential equations with spatial smoothing." SIAM J. Numer. Anal., 34(3), 1106–1126. (21 pages). http://dx.doi.org/10.1137/S0036142993256441.