Finite Element Methods For Nonlinear Parabolic Problems With Singularities

Many researchers have begun to study numerical methods and the corresponding mathematical theories to solve the elliptic and parabolic boundary value problems with singularities early from 1960s. They used symmetric and nonsymmetric finite element methods respectively on this class of linear or nonlinear problems, and obtained ideal results. Under the effect of numerical integrate ,a class of nonlinear parabolic boundary value problems with singular coefficients was considered in this article. First of all, existence and uniqueness of the weak solution of the variational problems was obtained. Secondly, weighted norm estimates considering and not considering the effect of numerical integrate were derived for semi-discrete problems. At last ,we obtained weighted L2 -norm estimate for whole-discrete problems.