Moving mesh for the axisymmetric harmonic map flow
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 4, p. 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 : https://doi.org/10.1051/m2an:2005034
Classification:  35A05,  35K55,  65N30,  65N50,  65N99
Keywords: moving mesh, finite elements, harmonic map flow, axisymmetric
@article{M2AN_2005__39_4_781_0,
     author = {Merlet, Benoit and Pierre, Morgan},
     title = {Moving mesh for the axisymmetric harmonic map flow},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
     pages = {781-796},
     doi = {10.1051/m2an:2005034},
     zbl = {1078.35008},
     mrnumber = {2165679},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_4_781_0}
}
Merlet, Benoit; Pierre, Morgan. Moving mesh for the axisymmetric harmonic map flow. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 4, pp. 781-796. doi : 10.1051/m2an:2005034. http://www.numdam.org/item/M2AN_2005__39_4_781_0/

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