Moving mesh for the axisymmetric harmonic map flow
ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 781-796.

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 L 2 -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.

DOI : 10.1051/m2an:2005034
Classification : 35A05, 35K55, 65N30, 65N50, 65N99
Mots-clés : moving mesh, finite elements, harmonic map flow, axisymmetric 
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Merlet, Benoit; Pierre, Morgan. Moving mesh for the axisymmetric harmonic map flow. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 781-796. doi : 10.1051/m2an:2005034. http://archive.numdam.org/articles/10.1051/m2an:2005034/

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