Local ultraconvergence of high order finite element method by interpolation postprocessing technique for elliptic problems with constant coefficients

摘要

Assume that u(x) satisfies the problem Lu(x) - partial derivative/partial derivative x(i)(a(ij)partial derivative u/partial derivative x(j)) = f(x), for all x is an element of Omega, u(x) = 0, for all x is an element of partial derivative Omega. In this article, using interpolation postprocessing technique, we will investigate the local ultraconvergence of the primal variable and the derivative of finite element approximation of u(x) using piecewise polynomials of degrees bi-k (k >= 3) over a rectangular partition. Assume that k >= 3 is odd and xo is an interior vertex satisfying rho(x(0), partial derivative Omega) >= c. Using the new interpolation postprocessing formula presented in this study, we show that the primal variable and the derivative of the post-processed finite element solution using piecewise of degrees bi-k (k >= 3) at xo converge to the primal variable and the derivative of the exact solution with order O(h(k+3) vertical bar 1n h vertical bar) under suitable regularity and mesh conditions, respectively. Finally, we use numerical experiments to illustrate our theoretical findings. (C) 2019 Elsevier Ltd. All rights reserved.