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Constraint preserving implicit finite element discretization of harmonic map flow into spheres
Author(s):
Sören
Bartels;
Andreas
Prohl.
Journal:
Math. Comp.
76
(2007),
1847-1859.
MSC (2000):
Primary 65M12, 65M60, 35K55, 35Q35
Posted:
May 24, 2007
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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
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
DOI:
10.1090/S0025-5718-07-02026-1
PII:
S 0025-5718(07)02026-1
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
Posted:
May 24, 2007
Additional Notes:
Supported by ``Deutsche Forschungsgemeinschaft'' through the DFG Research Center {\sc Matheon} ``Mathematics for key technologies'' in Berlin
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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