Constraint preserving implicit finite element discretization of harmonic map flow into spheres
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- by Sören Bartels and Andreas Prohl PDF
- Math. Comp. 76 (2007), 1847-1859 Request permission
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.References
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Additional Information
- Sören Bartels
- Affiliation: Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
- Email: sba@math.hu-berlin.de
- Andreas Prohl
- Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
- Email: prohl@na.uni-tuebingen.de
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1847-1859
- MSC (2000): Primary 65M12, 65M60, 35K55, 35Q35
- DOI: https://doi.org/10.1090/S0025-5718-07-02026-1
- MathSciNet review: 2336271