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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces
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by Sören Bartels PDF
Math. Comp. 79 (2010), 1263-1301 Request permission

Abstract:

This article studies the numerical approximation of harmonic maps into surfaces, i.e., critical points for the Dirichlet energy among weakly differentiable vector fields that are constrained to attain their pointwise values in a given manifold. An iterative algorithm that is based on a linearization of the constraint about the current iterate at the nodes of a triangulation is devised, and its global convergence to a discrete harmonic map is proved under general conditions. Weak accumulation of discrete harmonic maps at harmonic maps as discretization parameters tend to zero is established in two dimensions under certain assumptions on the underlying sequence of triangulations. Numerical simulations illustrate the performance of the algorithm for curved domains.
References
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Additional Information
  • Sören Bartels
  • Affiliation: Institute for Numerical Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstrasse 6, 53115 Bonn, Germany
  • Email: bartels@ins.uni-bonn.de
  • Received by editor(s): December 1, 2008
  • Received by editor(s) in revised form: May 8, 2009
  • Published electronically: September 16, 2009
  • © Copyright 2009 American Mathematical Society
  • Journal: Math. Comp. 79 (2010), 1263-1301
  • MSC (2000): Primary 65N12, 65N22, 58E20
  • DOI: https://doi.org/10.1090/S0025-5718-09-02300-X
  • MathSciNet review: 2629993