The Postprocessing, Maximum Norm Estimates And Superconvergence For Finite Element Methods To Nonlinear Equations Or Sobolev Type

In this paper, we consider finite element methods to the solution of three kinds of Sobolev equationsThe problem (1.1.1)is linear,(1.1.2) and (1.1.3)is nonlinear.The postprocessing for finite element solution is studied to equations of (1.1.1). The global superconvergence of first order for the error and its time derivatives is obtained in H1, W1,∞, L∞and Lp.For the (1.1.2)and (1.1.3), the stability of the Ritz-Volterra projection is discussed in W1,∞(Ω). Optimal order error estimates for any degree finite elements are obtaine in L∞(W1,∞(Ω))and L∞(L∞(Ω)), and superconvergence results for the approximate soli-tion given.