Moving mesh for the axisymmetric harmonic map flow
ESAIM: Mathematical Modelling and Numerical Analysis - 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 ${\mathrm{L}}^{2}$-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
Mots clés : 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},
pages = {781--796},
publisher = {EDP-Sciences},
volume = {39},
number = {4},
year = {2005},
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, Tome 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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