Optimal error estimates of mixed finite element methods for a fourth-order nonlinear elliptic problem

A mixed finite element method is developed for a nonlinear fourth-order elliptic problem. Optimal L2 error estimates are proved by using a special interpolation operator on the standard tensor-product finite elements of order k⩾1. Then two iterative schemes are presented and proved to keep the same optimal error estimates. Three numerical examples are provided to support the theoretical analysis.