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

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 77)

Abstract

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 \(\varOmega \subset \mathbb R^2\) and a 1d-finite-volume method on \(\partial \varOmega \). 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 \(L^\infty \left( 0,T,H^1(\varOmega )\right) \) whose trace is in \(L^\infty \left( 0,T,H^1(\partial \varOmega )\right) \).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373MarseilleFrance

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