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Numerische Mathematik

, Volume 119, Issue 3, pp 409–435 | Cite as

Error control for the approximation of Allen–Cahn and Cahn–Hilliard equations with a logarithmic potential

  • Sören Bartels
  • Rüdiger Müller
Article

Abstract

A fully computable upper bound for the finite element approximation error of Allen–Cahn and Cahn–Hilliard equations with logarithmic potentials is derived. Numerical experiments show that for the sharp interface limit this bound is robust past topological changes. Modifications of the abstract results to derive quasi-optimal error estimates in different norms for lowest order finite element methods are discussed and lead to weaker conditions on the residuals under which the conditional error estimates hold.

Mathematics Subject Classification (2000)

65M15 65M60 35K20 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut für Numerische SimulationRheinische Friedrich-Wilhelms-Universität BonnBonnGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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