A C0 weak Galerkin method for linear Cahn-Hilliard-Cook equation with random initial condition
A C0 weak Galerkin method for linear Cahn-Hilliard-Cook equation with random initial condition
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DOI：
10.1016/j.amc.2021.126659
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发表时间：
2022-02
期刊：
影响因子：
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通讯作者：
Shimin Chai;Yu Wang;Wenju Zhao;Yongkui Zou
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文献类型：
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作者：
Shimin Chai;Yu Wang;Wenju Zhao;Yongkui Zou
提出了求解线性Cahn-Hilliard-Cook方程的C 0弱Galerkin有限元方法.该方法的特点是避免了构造四阶问题C1有限元空间的复杂性，与完全间断弱Galerkin有限元方法相比，自由度明显减少。利用重新定义的离散弱拉普拉斯算子和经典的C 0拉格朗日元，得到了空间变量的L2最优误差估计.在时间上，采用经典的Euler格式进行数值模拟.最后，通过数值实验验证了所提出的数值方法的有效性。
This paper introduces a C 0 weak Galerkin finite element method for a linear Cahn–Hilliard–Cook equation. The highlights of the proposed method are that the complexity of constructing the C 1 finite element space for fourth order problem is avoided and the number of degree of freedom is apparently reduced compared to the fully discontinuous weak Galerkin finite element method. With the redefined discrete weak Laplace operator and the classical C 0 Lagrange elements, the L 2 optimal error estimates in spatial variable are obtained. In time, the classical Euler scheme is then used to do the numerical simulation. Finally, numerical experiments are presented to demonstrate the efficiency of the proposed numerical method.