A low order characteristic-nonconforming finite element method for nonlinear Sobolev equation with convection-dominated term

A low order nonconforming finite element method is combined with the method of characteristics to treat the nonlinear Sobolev equation with convection-dominated term. The optimal order error estimates in a broken H1-norm and L2-norm are obtained by some special properties of the interpolation operator and the mean value trick, 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 derived based on the interpolated postprocessing technique. The theoretical results are confirmed by some numerical experiments.