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Title: A saddle point approach to the computation of harmonic maps
Authors: Hu, Qiya
Tai, Xue Cheng
Winther, Ragnar
Keywords: DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
Issue Date: 2009
Source: Hu, Q., Tai, X. C., & Winther, R. (2009). A saddle point approach to the computation of harmonic maps. SIAM Journal on Numerical Analysis, 47(2), 1500-1523.
Series/Report no.: SIAM Journal on Numerical Analysis.
Abstract: In this paper we consider numerical approximations of a constraint minimization problem, where the object function is a quadratic Dirichlet functional for vector fields and the interior constraint is given by a convex function. The solutions of this problem are usually referred to as harmonic maps. The solution is characterized by a nonlinear saddle point problem, and the corresponding linearized problem is well-posed near strict local minima. The main contribution of the present paper is to establish a corresponding result for a proper finite element discretization in the case of two space dimensions. Iterative schemes of Newton type for the discrete nonlinear saddle point problems are investigated, and mesh independent preconditioners for the iterative methods are proposed.
ISSN: 0036-1429
DOI: 10.1137/060675575
Schools: School of Physical and Mathematical Sciences 
Rights: SIAM Journal on Numerical Analysis © copyright 2009 Siam Society for Industrial and Applied Mathematics. The journal's website is located at
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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