Finite Element Methods For Fourth Order Nonlinear Singular Elliptic Problems

The differential equations with singular coefficients are very important ones in physics,mechanic problems. The finite element method is a important method for solving such kind of problems.Early in 1960 s, many researchers have began to study the equation. In recent years, many methods solving the differential equation with singular coefficients have been proposed, such as finite difference method, symmetric finite element method, nonsymmetric finite element method. And they have achieved excellent results.In this paper, a class of fourth order nonlinear singular elliptic problems was considered. At first, existence and uniqueness of the weak solution of the variational problems is proved by using Banach fixed point theorem; second, error estimates in weighted H² norm, weighted L₂ norm, L₂ norm and L_∞ norm considering and not considering the effect of numerical integration; At last, considered the effect of numerical integration, error estimates in weighted H² norm was obtainded.