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 ...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.展开更多
基金supported in part by NSF(U.S.A.)under grants DMS-0712935 and DMS-1115118by NSERC(Canada)under discovery grant 311796.
文摘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.
