author = {Garcke, H. and Rumpf, M. and Weikard, U.},
  title = {The {C}ahn-{H}illiard Equation with Elasticity, Finite Element Approximation
	and Qualitative Analysis},
  journal = {Interfaces and Free Boundaries},
  year = {2001},
  volume = {3},
  pages = {101--118},
  number = {1},
  abstract = {We consider the Cahn-Hilliard equation - a fourth-order, nonlinear
	parabolic diffusion equation describing phase separation of a binary
	alloy which is quenched below a critical temperature. The occurrence
	of two phases is due to a nonconvex double well free energy. The
	evolution initially leads to a very fine microstructure of regions
	with different phases which tend to become coarser at later times.
	The resulting phases might have different elastic properties caused
	by a different lattice spacing. This effect is not reflected by the
	standard Cahn--Hilliard model. Here, we discuss an approach which
	contains anisotropic elastic stresses by coupling the expanded diffusion
	equation with a corresponding quasistationary linear elasticity problem
	for the displacements on the microstructure. Convergence and a discrete
	energy decay property are stated for a finite element discretization.
	An appropriate timestep scheme based on the strongly A-stable $\Theta$-scheme
	and a spatial grid adaptation by refining and coarsening improve
	the algorithms efficiency significantly. Various numerical simulations
	outline different qualitative effects of the generalized model. Finally,
	a surprising stabilizing effect of the anisotropic elasticity is
	observed in the limit case of a vanishing fourth order term, originally
	representing interfacial energy.},
  pdf = { 1}