In this paper, we develop a symmetric mixed covolume scheme for the nonlinear parabolic equations. The existence and uniqueness of the scheme are proved by using the lowest order Raviart–Thomas mixed element space on rectangular grids. We carry out a rigorous error estimates for the constructed scheme, establishing the first-order convergence for both velocity and pressure. Numerical examples are provided to verify that the numerical results are all in consistent with the theoretical analysis.

中文翻译：

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非线性抛物线问题的一种对称混合余量方法

在本文中，我们为非线性抛物线方程开发了一种对称混合余体积方案。利用矩形网格上的最低阶Raviart-Thomas混合元空间证明了该方案的存在性和唯一性。我们对构建的方案进行严格的误差估计，建立速度和压力的一阶收敛。给出数值算例验证数值结果均与理论分析一致。