Ultraconvergent Correction For Finite Element Of One Dimensional Variable Coefficients Problems

In this thesis, we study ultraconvergent corrected scheme of finite element approximation in one dimensional case (include variable coefficients two-point boundary value problem, variable coefficients parabolic problem of one space dimension). Even for quasi-uniform meshes, we obtain a globe ultraconvergent result in every element using the corrected scheme given in our paper. Through correcting, the convergent rate of stress and displacement increase 2, respectively.At first, we prove a theorem of finite element ultra-approximation.Next, for variable coefficients two-point boundary value problem, a ultra-convergent corrected scheme for finite element is obtained and proved directly by the method of requesting original function. And computational results demonstrate the theoretical finding.At last, for variable coefficients parabolic problem of one space dimension, we obtain a ultraconvergent corrected scheme for finite element using Ritz-Volterra projection and the time-dependent Green functions. Furthermore, we discussed a posterior error estimation.