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Moving mesh for the axisymmetric harmonic map flow

Published online by Cambridge University Press:  15 August 2005

Benoit Merlet  and
Morgan Pierre
Benoit Merlet
Affiliation:
ENS Cachan, Antenne de Bretagne, Avenue Robert Schumann, 35170 Bruz France. [email protected]
Morgan Pierre
Affiliation:
Laboratoire de Mathématiques, Université de Poitiers, Bd Marie et Pierre Curie, BP 30179, 86962 Futuroscope Cedex, France. [email protected] Centre de Mathématiques et de Leurs Applications, École Normale Supérieure de Cachan, 61 Av. du Président Wilson, 94235 Cachan Cedex, France.
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Abstract

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.

Keywords

Moving meshfinite elementsharmonic map flowaxisymmetric.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 4 , July 2005 , pp. 781 - 796
Copyright
© EDP Sciences, SMAI, 2005

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