Numerical approximations and error analysis of the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions

2020/07/24 by Xuelian Bao, Hui Zhang, Bao, Xuelian +1 · 1 citation
Materials Science · Mathematics · Computer Science · #Solidification and crystal growth phenomena #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2007.13546

Abstract

We consider numerical approximations and error analysis for the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions (P. Knopf et. al., arXiv, 2020). Based on the stabilized linearly implicit approach, a first-order in time, linear and energy stable scheme for solving this model is proposed. The corresponding semi-discretized-in-time error estimates for the scheme are also derived. Numerical experiments, including the comparison with the former work, the convergence results for the relaxation parameter K→0 and K→∞ and the accuracy tests with respect to the time step size, are performed to validate the accuracy of the proposed scheme and the error analysis.

Citations

• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows

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• Convergence analysis of positivity-preserving finite difference scheme for the Flory-Huggins-Cahn-Hilliard equation with dynamical boundary condition

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