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Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers


Authors: Sören Bartels, Christian Lubich and Andreas Prohl
Journal: Math. Comp. 78 (2009), 1269-1292
MSC (2000): Primary 65M12, 65M60, 35K55, 35Q35
DOI: https://doi.org/10.1090/S0025-5718-09-02221-2
Published electronically: February 18, 2009
MathSciNet review: 2501050
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Abstract: We propose fully discrete schemes to approximate the harmonic map heat flow and wave maps into spheres. The finite-element based schemes preserve a unit length constraint at the nodes by means of approximate discrete Lagrange multipliers, satisfy a discrete energy law, and iterates are shown to converge to weak solutions of the continuous problem. Comparative computational studies are included to motivate finite-time blow-up behavior in both cases.


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Additional Information

Sören Bartels
Affiliation: Institute for Numerical Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstraße 6, D-53115 Bonn, Germany
Email: bartels@ins.uni-bonn.de

Christian Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: lubich@na.uni-tuebingen.de

Andreas Prohl
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: prohl@na.uni-tuebingen.de

DOI: https://doi.org/10.1090/S0025-5718-09-02221-2
Received by editor(s): April 10, 2007
Received by editor(s) in revised form: April 30, 2008
Published electronically: February 18, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.