Paper Info
Title
Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces.
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.
Year
DOI
Venue
2010
10.1090/S0025-5718-09-02300-X
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
numerical analysis,finite element,numerical simulation,iterative algorithm,two dimensions,harmonic map,critical point,vector field
Discretization,Harmonic function,Mathematical optimization,Harmonic map,Mathematical analysis,Triangulation (social science),Dirichlet's energy,Linearization,Mathematics,Harmonic measure,Pointwise
Journal
Volume
Issue
ISSN
79
271
0025-5718
Citations 
PageRank 
References 
4
0.49
5
Authors
1
Name
Order
Citations
PageRank
Sören Bartels135556.90