Finite Element Methods For One Dimensional Nonlinear Parabolic Problems With Singularities

In this article ,The finite element method for a class of singular nonlinear parabolic problem was considered. First of all,we gave out the definition of weighted Sobolev space,and existence and uniqueness of the weak solution of the variational problems is proved.Secondly,Then the weighted L₂ norm ,weighted L₂ norm , L₂ norm,L_∞ norm estimates for semi-discrete problems were obtained .At last,error estimates in weighted L₂ norm are derived for whole-discrete problems.