A constraint preserving numerical method for the approximation of wave maps into spheres is presented. The scheme has a second order consistency property and is energy preserving and reversible. Its unconditional convergence to an exact solution is proved. A fixed point iteration allows for a solution of the nonlinear system of equations in each time step under a moderate step size restriction.
DOI : 10.1051/m2an/2014044
Mots-clés : Geometric evolution problem, wave maps, nonlinear partial differential equation, discretization
@article{M2AN_2015__49_2_551_0,
author = {Bartels, S\"oren},
title = {Fast and accurate finite element approximation of wave maps into spheres},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {551--558},
publisher = {EDP-Sciences},
volume = {49},
number = {2},
year = {2015},
doi = {10.1051/m2an/2014044},
mrnumber = {3342217},
zbl = {1316.65085},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014044/}
}
TY - JOUR AU - Bartels, Sören TI - Fast and accurate finite element approximation of wave maps into spheres JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 551 EP - 558 VL - 49 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014044/ DO - 10.1051/m2an/2014044 LA - en ID - M2AN_2015__49_2_551_0 ER -
%0 Journal Article %A Bartels, Sören %T Fast and accurate finite element approximation of wave maps into spheres %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 551-558 %V 49 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014044/ %R 10.1051/m2an/2014044 %G en %F M2AN_2015__49_2_551_0
Bartels, Sören. Fast and accurate finite element approximation of wave maps into spheres. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 551-558. doi : 10.1051/m2an/2014044. http://www.numdam.org/articles/10.1051/m2an/2014044/
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