Finite Element Method For General Two-Dimentional Nonlinear Singular Problems

The equations with singular coefficients are very impor-tant ones in practical problems. Such as in nuclear plysics, gasdynamics, mechanics,boundary layer theory,nonlinear field and optics.The finite element method is a important method for solving such kindof problems. Early in 1960s,many for researchers have began to studythe equation.In resent years, many methods solving the differentialequation with singular coefficients have been proposed,such a finitedifference method,symmetric finite element method. And they haveachieved excellent results.In this article,a class of general two-dimentional nonli-near boundary with singular coefficient is considered.First ofall,existence and uniqueness of the weak solution of the variationalproblems is proved by using Banach fixed point theorem. Secondly, theprior estimate of finite element solution, the error estimates inweighted L~2 norm and H~1 norm not considering the effect of numericalintegration. At last, the error estimate in weighted H~1 norm ofconsidering the effect of numerical integration.