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Burman, Erik; Kessler, Daniel; Rappaz, Jacques

Convergence of the finite element method applied to an anisotropic phase-field model. (English) Zbl 1155.74404

Ann. Math. Blaise Pascal 11, No. 1, 67-94 (2004).
Summary: 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 \(H^1\)-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 converge.

Cited in 2 Documents

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E10 Anisotropy in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Software:

ALBERT
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\textit{E. Burman} et al., Ann. Math. Blaise Pascal 11, No. 1, 67--94 (2004; Zbl 1155.74404)
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References:

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