In this paper, we discuss a priori error estimates of two-grid mixed finite element methods for a class of nonlinear parabolic equations. The lowest order Raviart-Thomas mixed finite element and Crank-Nicolson scheme are used for the spatial and temporal discretization. First, we derive the optimal a priori error estimates for all variables. Second, we present a two-grid scheme and analyze its convergence. It is shown that if the two mesh sizes satisfy h = H², then the two-grid method achieves the same convergence property as the Raviart-Thomas mixed finite element method. Finally, we give a numerical example to verify the theoretical results.

中文翻译：

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一类非线性抛物方程的两网格Raviart-Thomas混合有限元方法与Crank-Nicolson方案

在本文中，我们讨论了一类非线性抛物方程的两网格混合有限元方法的先验误差估计。最低阶Raviart-Thomas混合有限元和Crank-Nicolson方案用于空间和时间离散化。首先，我们得出所有变量的最优先验误差估计。其次，我们提出一个两网格方案并分析其收敛性。结果表明，如果两个网格大小均满足h = H ²，则二重网格方法将获得与Raviart-Thomas混合有限元方法相同的收敛性。最后，我们给出一个数值例子来验证理论结果。