Nonconforming Morley finite element method is applied to a fourth order nonlinear reaction-diffusion problems. After deriving some regularity results to be used subsequently in our error analysis, Morley FEM is employed to discretize in the spatial direction to obtain a semidiscrete problem. A priori bounds for the discrete solution are derived and with the help of an auxiliary problem, optimal error estimates are proved for the semidiscrete scheme. Based on backward Euler method, a completely discrete scheme is analysed and wellposedness of the discrete problem is discussed. A priori error bounds are derived. It is observed that constants do not depend exponentially on the inverse of a small parameter appeared as the coefficient in the fourth order term and all the results are derived when the initial data are in $H_0^2$. Finally, some computational experiments are conducted to confirm our theoretical findings.

非一致性 Morley 有限元方法应用于四阶非线性反应扩散问题。在推导出一些随后用于我们的误差分析的规律性结果后，使用 Morley FEM 在空间方向上进行离散化以获得半离散问题。推导出离散解的先验界限，并在辅助问题的帮助下，证明了半离散方案的最佳误差估计。基于后向欧拉方法，分析了一个完全离散的方案，讨论了离散问题的适定性。先验误差界限被推导出来。可以看出，常数不以指数方式依赖于作为四阶项中系数出现的小参数的倒数，所有结果都是在初始数据为$H_0^2$. 最后，进行了一些计算实验以证实我们的理论发现。