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Constraint preserving implicit finite element discretization of harmonic map flow into spheres

Authors: Sören Bartels and Andreas Prohl
Journal: Math. Comp. 76 (2007), 1847-1859
MSC (2000): Primary 65M12, 65M60, 35K55, 35Q35
Published electronically: May 24, 2007
MathSciNet review: 2336271
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Abstract: Discretization of the harmonic map flow into spheres often uses a penalization or projection strategy, where the first suffers from the proper choice of an additional parameter, and the latter from the lack of a discrete energy law, and restrictive mesh-constraints. We propose an implicit scheme that preserves the sphere constraint at every node, enjoys a discrete energy law, and unconditionally converges to weak solutions of the harmonic map heat flow.

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Additional Information

Sören Bartels
Affiliation: Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany

Andreas Prohl
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Keywords: Harmonic map flow, finite element method, fully discrete scheme, convergence.
Received by editor(s): October 10, 2005
Received by editor(s) in revised form: September 11, 2006
Published electronically: May 24, 2007
Additional Notes: Supported by “Deutsche Forschungsgemeinschaft” through the DFG Research Center Matheon “Mathematics for key technologies” in Berlin
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.