Numerische Mathematik

, Volume 100, Issue 4, pp 639–662

Numerical approximation of the Cahn-Larché equation

Article

Summary

Spinodal decomposition, i.e., the separation of a homogeneous mixture into different phases, can be modeled by the Cahn-Hilliard equation - a fourth order semilinear parabolic equation. If elastic stresses due to a lattice misfit become important, the Cahn-Hilliard equation has to be coupled to an elasticity system to take this into account. Here, we present a discretization based on finite elements and an implicit Euler scheme. We first show solvability and uniqueness of solutions. Based on an energy decay property we then prove convergence of the scheme. Finally we present numerical experiments showing the impact of elasticity on the morphology of the microstructure.

Mathematics Subject Classification(2000)

35K35 35K55 65L50 65M12 65M15 65M60 82B26 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Naturwissenschaftliche Fakultät I - MathematikUniversität RegensburgRegensburgGermany
  2. 2.Institut für MathematikUniversität Duisburg-EssenDuisburgGermany

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