Volume 39, Number 4, July-August 2005
|Page(s)||781 - 796|
|Published online||15 August 2005|
Moving mesh for the axisymmetric harmonic map flow
ENS Cachan, Antenne de Bretagne,
Avenue Robert Schumann,
35170 Bruz France. email@example.com
2 Laboratoire de Mathématiques, Université de Poitiers, Bd Marie et Pierre Curie, BP 30179, 86962 Futuroscope Cedex, France. Morgan.Pierre@math.univ-poitiers.fr
3 Centre de Mathématiques et de Leurs Applications, École Normale Supérieure de Cachan, 61 Av. du Président Wilson, 94235 Cachan Cedex, France.
Revised: 2 March 2005
We build corotational symmetric solutions to the harmonic map flow from the unit disc into the unit sphere which have constant degree. First, we prove the existence of such solutions, using a time semi-discrete scheme based on the idea that the harmonic map flow is the L2-gradient of the relaxed Dirichlet energy. We prove a partial uniqueness result concerning these solutions. Then, we compute numerically these solutions by a moving-mesh method which allows us to deal with the singularity at the origin. We show numerical evidence of the convergence of the method.
Mathematics Subject Classification: 35A05 / 35K55 / 65N30 / 65N50 / 65N99
Key words: Moving mesh / finite elements / harmonic map flow / axisymmetric.
© EDP Sciences, SMAI, 2005
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