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A Numerical Study of Blowup in the Harmonic Map Heat Flow Using the MMPDE Moving Mesh Method

Published online by Cambridge University Press:  28 May 2015

Ronald D. Haynes ,
Weizhang Huang  and
Paul A. Zegeling
Ronald D. Haynes*
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada
Weizhang Huang*
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
Paul A. Zegeling*
Affiliation:
Department of Mathematics, Utrecht University, Utrecht, The Netherlands
*
Corresponding author.Email address:rhaynes@mun.ca
Corresponding author.Email address:huang@math.ku.edu
Corresponding author.Email address:P.A.Zegeling@uu.nl
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Abstract

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method. A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic analysis. Moreover, the moving mesh method has finite time blowup when the underlying continuous problem does. In situations where the continuous problem has infinite time blowup, the moving mesh method exhibits finite time blowup with a blowup time tending to infinity as the number of mesh points increases. The inadequacy of a uniform mesh solution is clearly demonstrated.

Keywords

35K9165M5065M06Heat flowharmonic mapblowupmoving mesh methodfinite difference
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 2 , May 2013 , pp. 364 - 383
Copyright
Copyright © Global Science Press Limited 2013

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