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Numerische Mathematik

, Volume 109, Issue 4, pp 489–507 | Cite as

Convergence of an implicit, constraint preserving finite element discretization of p-harmonic heat flow into spheres

  • Sören Bartels
  • Andreas Prohl
Article

Abstract

We propose an implicit discretization of the p-harmonic map heat flow into the sphere S 2 that enjoys a discrete energy inequality and converges under only a mild mesh constraint to a weak solution. A fully practical iterative scheme that approximates the solution of the nonlinear system of equations in each time step is proposed and analyzed. Computational studies to motivate possible finite-time blow-up behavior of solutions for p ≠ 2 are included.

Mathematics Subject Classification (2000)

65M12 65M60 35K55 35Q35 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut für Numerische SimulationUniversität BonnBonnGermany
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany

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