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Moving mesh partial differential equations (MMPDEs) based upon the equidistribution principle
Huang, Weizhang Ren, Yuhe Russell, Robert D.
Huang, Weizhang
Ren, Yuhe
Russell, Robert D.
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Abstract
This paper considers several moving mesh partial differential equations that are related to the equidistribution principle. Several of these are new, and some correspond to discrete moving mesh equations that have been used by others. Their stability is analyzed and it is seen that a key term for most of these moving mesh PDEs is a source-like term that measures the level of equidistribution. It is shown that under weak assumptions mesh crossing cannot occur for most of them. Finally, numerical experiments for these various moving mesh PDEs are performed to study their relative properties.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/0731038.
Date
1994-06-01
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Society for Industrial and Applied Mathematics
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Keywords
equidistribution, moving mesh PDE, adaption
Citation
Huang, Weizhang., Ren, Yuhe., Russell, Robert D., "Moving mesh partial differential equations (MMPDEs) based upon the equidistribution principle." SIAM J. Numer. Anal., 31(3), 709–730. (22 pages). http://dx.doi.org/10.1137/0731038.