Fast and accurate finite element approximation of wave maps into spheres
Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität
Freiburg, Hermann-Herder Str.
Received: 13 March 2014
Revised: 14 August 2014
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.
Mathematics Subject Classification: 65N12 / 58J45 / 35L70 / 35Q75
Key words: Geometric evolution problem / wave maps / nonlinear partial differential equation / discretization
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