Fourier Spectral Approximation to Global Attractor for 2D Convective Cahn–Hilliard Equation

Zhao, Xiaopeng

doi:10.1007/s40840-016-0378-3

Cited by 5 publications

(3 citation statements)

References 39 publications

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“…Интерес к изучению существования и аппроксимации аттракторов не ослабевает (см. [15,37,67,78,97,100,139,237,278,279]). Хорошо известен стандартный результат теории динамических систем, согласно которому аттракторы параметрических динамических систем сходятся полунепрерывно сверху по параметру (см.…”

Section: сходимость аттракторовunclassified

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

Piskarev¹,

Ovchinnikov²

2021

Итоги науки и техники. Серия «Современная математика и ее прило

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В обзоре обсуждаются такие разделы теории аппроксимации абстрактных дифференциальных уравнений как аппроксимация аттракторов в случае гиперболических стационарных точек, затенение и аппроксимация дробных по времени полулинейных задач.

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Section: сходимость аттракторовunclassified

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

Piskarev¹,

Ovchinnikov²

2021

Итоги науки и техники. Серия «Современная математика и ее прило

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“…ere have been many research papers regarding the accurate numerical methods for the CH equation [15][16][17][18] (see the references therein for more details). In particular, a comparison study among various numerical methods for the CH equation was conducted on the perspective of stability and efficiency [19].…”

Section: Introductionmentioning

confidence: 99%

A Simple Benchmark Problem for the Numerical Methods of the Cahn–Hilliard Equation

Lee

Wang

et al. 2021

Discrete Dynamics in Nature and Society

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We present a very simple benchmark problem for the numerical methods of the Cahn–Hilliard (CH) equation. For the benchmark problem, we consider a cosine function as the initial condition. The periodic sinusoidal profile satisfies both the homogeneous and periodic boundary conditions. The strength of the proposed problem is that it is simpler than the previous works. For the benchmark numerical solution of the CH equation, we use a fourth-order Runge–Kutta method (RK4) for the temporal integration and a centered finite difference scheme for the spatial differential operator. Using the proposed benchmark problem solution, we perform the convergence tests for an unconditionally gradient stable scheme via linear convex splitting proposed by Eyre and the Crank–Nicolson scheme. We obtain the expected convergence rates in time for the numerical schemes for the one-, two-, and three-dimensional CH equations.

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“…considered properties of solutions for the initial-boundary value problem of the convective Cahn-Hilliard equation with nonconstant mobility and degenerate mobility. There are also some papers related to the numerical solutions for the convective Cahn-Hilliard equation, please refer to [51,1] and the reference there in.…”

Section: Introductionmentioning

confidence: 99%

Global well-posedness of solutions to the Cauchy problem of convective Cahn–Hilliard equation

Zhao

2018

Annali di Matematica

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In this paper, we consider the global well-posedness and time-decay rates of solution to the Cauchy problem for 3D convective Cahn-Hilliard equation with doublewell potential via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, theḢ −s (0 < s ≤ 1 2 ) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.2010 Mathematics Subject Classification. 35Q35, 35B65, 76N10, 76D05.

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Fourier Spectral Approximation to Global Attractor for 2D Convective Cahn–Hilliard Equation

Abstract: In this paper, we consider the Fourier spectral method for numerically solving the 2D convective Cahn-Hilliard equation. The semi-discrete and fully discrete schemes are established. Moreover, the existence, uniqueness and the optimal error bound are also considered.

Cited by 5 publications

References 39 publications

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

A Simple Benchmark Problem for the Numerical Methods of the Cahn–Hilliard Equation

Global well-posedness of solutions to the Cauchy problem of convective Cahn–Hilliard equation

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