We formulate a finite element method for the computation of solutions to an anisotropic phase-field model for a binary alloy. Convergence is proved in the -norm. The convergence result holds for anisotropy below a certain threshold value. We present some numerical experiments verifying the theoretical results. For anisotropy below the threshold value we observe optimal order convergence, whereas in the case where the anisotropy is strong the numerical solution to the phase-field equation does not...
Phase-field models, the simplest of which is Allen–Cahn’s problem, are characterized by a small parameter that dictates the interface thickness. These models naturally call for mesh adaptation techniques, which rely on a posteriori error control. However, their error analysis usually deals with the underlying non-monotone nonlinearity via a Gronwall argument which leads to an exponential dependence on . Using an energy argument combined with a topological continuation argument and a spectral...
Phase-field models, the simplest of which is Allen–Cahn's
problem, are characterized by a small parameter that dictates
the interface thickness. These models naturally call for mesh adaptation
techniques, which rely on error control.
However, their error analysis usually deals with the
underlying non-monotone nonlinearity via a Gronwall argument which
leads to an exponential dependence on ε. Using an energy argument
combined with a
topological continuation argument and a spectral estimate,...
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