Free access
Issue
ESAIM: M2AN
Volume 39, Number 4, July-August 2005
Page(s) 781 - 796
DOI http://dx.doi.org/10.1051/m2an:2005034
Published online 15 August 2005
  1. F. Alouges and M. Pierre, Mesh optimization for singular axisymmetric harmonic maps from the disc into the sphere. Numer. Math. To appear.
  2. F. Bethuel, J.-M. Coron, J.-M. Ghidaglia and A. Soyeur, Heat flows and relaxed energies for harmonic maps, in Nonlinear diffusion equations and their equilibrium states, 3 (Gregynog, 1989), Birkhäuser Boston, Boston, MA. Progr. Nonlinear Differential Equations Appl. 7 (1992) 99–109.
  3. M. Bertsch, R. Dal Passo and R. van der Hout, Nonuniqueness for the heat flow of harmonic maps on the disk. Arch. Rational Mech. Anal. 161 (2002) 93–112. [CrossRef]
  4. H. Brezis and J.-M. Coron, Large solutions for harmonic maps in two dimensions. Comm. Math. Phys. 92 (1983) 203–215. [CrossRef] [MathSciNet]
  5. N. Carlson and K. Miller, Design and application of a gradient-weighted moving finite element code. I. In one dimension. SIAM J. Sci. Comput. 19 (1998) 728–765. [CrossRef] [MathSciNet]
  6. K.-C. Chang, Heat flow and boundary value problem for harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989) 363–395.
  7. J. Eells and J. Sampson, Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86 (1964) 109–160. [CrossRef] [MathSciNet]
  8. A. Freire, Uniqueness for the harmonic map flow from surfaces to general targets. Comment. Math. Helv. 70 (1995) 310–338. [CrossRef] [MathSciNet]
  9. A. Freire, Uniqueness for the harmonic map flow in two dimensions. Calc. Var. Partial Differential Equations 3 (1995) 95–105. [CrossRef] [MathSciNet]
  10. F. Hülsemann and Y. Tourigny, A new moving mesh algorithm for the finite element solution of variational problems. SIAM J. Numer. Anal. 35 (1998) 1416–1438. [CrossRef] [MathSciNet]
  11. M. Pierre, Weak BV convergence of moving finite elements for singular axisymmetric harmonic maps. SIAM J. Numer. Anal. To appear.
  12. E. Polak, Algorithms and consistent approximations, Optimization, Applied Mathematical Sciences 124 (1997), Springer-Verlag, New York.
  13. J. Qing, On singularities of the heat flow for harmonic maps from surfaces into spheres. Comm. Anal. Geom. 3 (1995) 297–315. [MathSciNet]
  14. S. Rippa and B. Schiff, Minimum energy triangulations for elliptic problems. Comput. Methods Appl. Mech. Engrg. 84 (1990) 257–274. [CrossRef] [MathSciNet]
  15. M. Struwe, The evolution of harmonic maps, in Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990). Math. Soc. Japan (1991) 1197–1203.
  16. P. Topping, Reverse bubbling and nonuniqueness in the harmonic map flow. Internat. Math. Res. Notices 10 (2002) 505–520. [CrossRef]

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