TY - JOUR
T1 - A Numerical Study of Blowup in the Harmonic Map Heat Flow Using the MMPDE Moving Mesh Method
AU - Ronald D. Haynes, Weizhang Huang & Paul A. Zegeling
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 364
EP - 383
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1130nm
UR - https://global-sci.org/intro/article_detail/nmtma/5909.html
KW - Heat flow, harmonic map, blowup, moving mesh method, finite difference.
AB - <p style="text-align: justify;">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. &nbsp;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 &nbsp;of a uniform mesh solution is clearly demonstrated.</p>