# Moving mesh for the axisymmetric harmonic map flow

- Volume: 39, Issue: 4, page 781-796
- ISSN: 0764-583X

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topMerlet, Benoit, and Pierre, Morgan. "Moving mesh for the axisymmetric harmonic map flow." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.4 (2005): 781-796. <http://eudml.org/doc/245389>.

@article{Merlet2005,

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 $\mathrm \{L\}^\{2\}$-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.},

author = {Merlet, Benoit, Pierre, Morgan},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {moving mesh; finite elements; harmonic map flow; axisymmetric; corotational initial data; corotational degree},

language = {eng},

number = {4},

pages = {781-796},

publisher = {EDP-Sciences},

title = {Moving mesh for the axisymmetric harmonic map flow},

url = {http://eudml.org/doc/245389},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Merlet, Benoit

AU - Pierre, Morgan

TI - Moving mesh for the axisymmetric harmonic map flow

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 4

SP - 781

EP - 796

AB - 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.

LA - eng

KW - moving mesh; finite elements; harmonic map flow; axisymmetric; corotational initial data; corotational degree

UR - http://eudml.org/doc/245389

ER -

## References

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