Error Estimate of Exponential Time Differencing Runge-Kutta Scheme for the Epitaxial Growth Model Without Slope Selection

Sun, Yabing; Zhou, Quan

doi:10.1007/s10915-022-01977-7

J Sci Comput

2022

DOI: 10.1007/s10915-022-01977-7

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Error Estimate of Exponential Time Differencing Runge-Kutta Scheme for the Epitaxial Growth Model Without Slope Selection

Yabing Sun

Quan Zhou

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2024

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Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations

Duan,

Li,

Qiao

2024

Numerical Methods Partial

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In this article, we develop stable and efficient numerical schemes for a binary fluid‐surfactant phase‐field model which consists of two Cahn–Hilliard type equations with respect to the free energy containing a Ginzburg–Landau double‐well potential, a logarithmic Flory–Huggins potential and a nonlinear coupling entropy. The numerical schemes, which are decoupled and linear, are established by the central difference spatial approximation in combination with the first‐ and second‐order exponential time differencing methods based on the convex splitting of the free energy. For the sake of the linearity of the schemes, the nonlinear terms, especially the logarithmic term, are approximated explicitly, which requires the bound preservation of the numerical solution to make the algorithm robust. We conduct the convergence analysis and prove the bound‐preserving property in details for both first‐ and second‐order schemes, where the high‐order consistency analysis is applied to the first‐order case. In addition, the energy stability is also obtained by the nature of the convex splitting. Numerical experiments are performed to verify the accuracy and stability of the schemes and simulate the dynamics of phase separation and surfactant adsorption.

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Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations

Duan,

Li,

Qiao

2024

Numerical Methods Partial

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show abstract

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Error Estimate of Exponential Time Differencing Runge-Kutta Scheme for the Epitaxial Growth Model Without Slope Selection

Cited by 1 publication

References 32 publications

Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations

Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations

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