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Nonsmooth Schur-Newton methods for vector-valued Cahn-Hilliard equations

Please always quote using this URN:urn:nbn:de:0296-matheon-10394
  • We introduce nonsmooth Schur-Newton methods for the solution of the nonlinear discrete saddle-point problems arising from discretized vector-valued Cahn-Hilliard equations with logarithmic and obstacle potentials. The discrete problems are obtained by semi-implicit discretization in time and a first order finite element discretization in space. We incorporate the linear constraints that enforce solutions to stay on the Gibbs simplex using Lagrangian multipliers and prove existence of these multipliers under the assumption of a non-trivial initial condition for the order parameters.

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Metadaten
Author:Carsten Gräser, Ralf Kornhuber, Uli Sack
URN:urn:nbn:de:0296-matheon-10394
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/30
Release Date:2012/01/30
Institute:Research Center Matheon
Freie Universität Berlin
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K55 Nonlinear parabolic equations
Preprint Number:904
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