# Moving mesh for the axisymmetric harmonic map flow

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 39.4 (2010): 781-796. <http://eudml.org/doc/194286>.

@article{Merlet2010,

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.
},

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

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

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

language = {eng},

month = {3},

number = {4},

pages = {781-796},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/194286},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Merlet, Benoit

AU - Pierre, Morgan

TI - Moving mesh for the axisymmetric harmonic map flow

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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 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.

LA - eng

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

UR - http://eudml.org/doc/194286

ER -

## References

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