Nonconforming Finite Element Methods For Sobolev Equations And Variational Inequality

In this paper, a low order nonconforming finite element method is combined with the method of characteristics to treat the nonlinear Sobolev equations with convection-dominated term. The optimal error estimates in the energy norm and L~2-norm are obtained by using some special properties of the interpolation operator and the mean value technique, instead of the so-called elliptic projection which is an indispensable tool in the convergence analysis of the previous literature. In addition, the global superconvergence is obtained based on the interpolated postprocessing technique. At last, a general error estimate formulation of nonconforming finite element method with full-discrete scheme is proposed for the parabolic variational inequality. The optimal error estimate is obtained.