A Ciarlet-Raviart type isoparametric mixed finite element method (MFEM) is constructed and analyzed for solving a class of fourth-order elliptic equation with Navier boundary condition defined on a curved domain in ${\mathbb{R}}^2$, and numerical quadrature is also considered in the scheme. The existence and uniqueness of the numerical solutions are proved under certain numerical quadrature. With the help of the special technically analysis, the optimal error estimates with $H^1$ norm are obtained in ${\mathrm{\Omega }}_h$, which yields better accuracy than using a convex polygonal domain to approximate the curved domain. For either constant coefficients or nonconstant coefficients problem, numerical examples are listed to confirm theoretical analysis respectively.

构造并分析了Ciarlet-Raviart型等参混合有限元方法（MFEM），用于求解一类具有Navier边界条件的四阶椭圆方程。 ${\mathbb{[R}}^{\mathrm{2个}}$，并且在该方案中还考虑了数字正交。在一定的数值​​正交条件下，证明了数值解的存在性和唯一性。借助特殊的技术分析，可以估算出最佳误差$H^{\mathrm{1个}}$ 规范是在 ${\mathrm{\Omega }}_H$，与使用凸多边形区域逼近弯曲区域相比，该方法产生的精度更高。对于常数系数或非常数系数问题，分别列出了数值示例来确认理论分析。