Finite Element Methods For Two Dimensional Nonlinear Parabolic Problems With Singularities

The finite element method is now a classical method for solving the partial differential equations arising in various contexts of science and technology.The partial differential equations with singular coefficients are important ones in practical problems. In recent years,many methods solving the partial differential equations with singular coefficients have been proposed,such as finite difference method,symmetric finite element method,nonsymmetric finite element method and so on ;some ideal results have been obtained.In this article, a class of nonlinear parabolic boundary problemes with two singular coefficients in two dimensional domain is considered.First of all, existence and uniqueness of the weak solution of the variational problems is proved.Secondly,error estimates in weighted norm considering and not considering the effect of numerical integration are both estabished for semi-discrete problems.At last,error estimates in weighted L₂ norm are derived for whole-discrete problems.