A mixed finite element method is developed for a semilinear fourth-order elliptic boundary value problem. The existence and uniqueness of the solutions to the mixing problem are proved by constructing an auxiliary problem. Moreover, a computational format is provided for numerical calculation, the convergence of this problem is proved under some hypothetical conditions. The optimal error estimate of the semilinear fourth-order elliptic boundary value problem is analyzed by a two-grid method. Finally, some numerical examples are provided to support the theoretical analysis.

中文翻译：

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半线性四阶问题的混合元素计算方案

针对半线性四阶椭圆边值问题，提出了一种混合有限元方法。通过构造一个辅助问题，证明了混合问题解的存在性和唯一性。此外，为数值计算提供了一种计算格式，在某些假设条件下证明了该问题的收敛性。通过二重网格法分析了半线性四阶椭圆边值问题的最优误差估计。最后，提供了一些数值示例来支持理论分析。