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

摘要

A mixed finite element method is developed for a nonlinear fourth-order elliptic problem. Optimal L-2 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. (c) 2006 Elsevier Inc. All rights reserved.