Finite-volume method for the Cahn-Hilliard equation with dynamic boundary conditions

Nabet, Flore

doi:10.1051/proc/201445052

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2014

2023

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Cited by 2 publications

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“…To this end, we adapt the proof of Theorem A.2 in [5] and we use the particular form of the extension operator φ and the coupling between the domain Ω and its boundary Γ . Then, thanks to the a priori estimates on the solutions (see [8]…”

Section: Theorem 2 (Estimation Of Space Translates) There Exists An mentioning

confidence: 99%

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Finite-Volume Analysis for the Cahn-Hilliard Equation with Dynamic Boundary Conditions

Nabet¹

2014

Springer Proceedings in Mathematics &Amp; Statistics

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This work is devoted to the convergence analysis of a finite-volume approximation of the 2D Cahn-Hilliard equation with dynamic boundary conditions. The method that we propose couples a 2d-finite-volume method in a bounded, smooth domain Ω ⊂ R 2 and a 1d-finite-volume method on ∂ Ω . We prove convergence of the sequence of approximate solutions. One of the main ingredient is a suitable space translation estimate that gives a limit in L ∞ 0, T, H 1 (Ω ) whose trace is in L ∞ 0, T, H 1 (∂ Ω ) .

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Section: Theorem 2 (Estimation Of Space Translates) There Exists An mentioning

confidence: 99%

“…In [8], we give numerical experiments with different choices of parameters and surface potential f s that show the different expected qualitative behavior of the solutions. In this paper, we focus on the numerical error estimates.…”

Section: Numerical Testsmentioning

confidence: 99%