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Robust Error Estimates for Adaptive Phase Field Simulations
Author(s) -
Bartels Sören,
Müller Rüdiger
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810983
Subject(s) - phase (matter) , rotor (electric) , field (mathematics) , phase field models , exponential growth , materials science , soldering , interface (matter) , mechanics , mathematics , statistical physics , mechanical engineering , physics , metallurgy , engineering , mathematical analysis , bubble , quantum mechanics , maximum bubble pressure method , pure mathematics
Abstract Phase field equations are commonly used as a regularized model, where bulk phases are separated by interface regions that have a thickness of the order γ. Their numerical analysis is well established for a fixed parameter size γ, but conventional error estimates depend exponentially on γ −1 and thus become useless in the relevant case if γ→0. Technical applications include e.g. the simulation of Sn–Cu alloys for the production of lead free solder or Ni–Al alloys used for rotor blade surfaces. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)