Numerische Mathematik

, Volume 100, Issue 4, pp 639-662

First online:

Numerical approximation of the Cahn-Larché equation

  • Harald GarckeAffiliated withNaturwissenschaftliche Fakultät I - Mathematik, Universität Regensburg Email author 
  • , Ulrich WeikardAffiliated withInstitut für Mathematik, Universität Duisburg-Essen

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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