On Superconvergence Properties And Postprocess Of Finite Element Approximation Of Non-smooth Solutions In One Dimensional

In this paper,the superconvergence properties and postprocess techniques offinite dement approximation of non-smooth solutions in one dimensional problemis discussed.Firstly, acording to the fatal flaws of classical theory of finite element supercon-vergence, using the projection-type interpolation, we defined a new order of errorestimate, and the rationality is verified.Secondly, for a class of two-point boundary value problems, based on the neworder of error estimate, two basic estimate are obtained on the condition of so-lutions is not smooth. Natural superconvergence properties are also obtained byusing the theory of discrete Green's function. The numerical experiments showedthat phenomenon of superclose and superconvergence does exist in finite elementapproximation of non-smooth solutions.Lastly, the superconvergence postprocess technique of FEM is discussed. Thisis the core part of this paper. Through interpolation postprocess, SPR postprocessand corrected scheme given in this paper, globe superconvergent or ultraconvergentresults in every element or element patch are obtained. The a posteriori errorestimate is also discussed.