Postprocessing Technique For Odd-degree Rectangular Finite Elements

In 1992 Zienkiewicz and Zh[34]-[38] proposed the supercon-vergence patch recovery, i.e. the SPR technique. Because of its advantage, such as its simplicity of its implementation, easiness to understand, convenience to access to the finite element application software etc., it has been generally applied by the engineering circle, and is thought of, by Babuska etc., as one of the most robust posterior error estimators which are asymptotically exact.It is of interest to note that the ultraconvergence, i.e. with two order higher than the global optimal convergent rate, of the derivatives at the points of interest is obtained by the SPR technique for all even-order elements on the uniform meshes in either one or two situation. But the pity is that only superconvergence, not ultraconvergence, is achieved by this method for odd-order finite elements.This paper analysizes the SPR technique for odd-order finite elements in details, and improves it. In this paper, the numerical tests indicate that the ultraconvergence can be obtained by a new derivative recovery produre, and the results is justified theoretically.In the second chapter a new derivative recovery operator is constructed. Numerical testes show that the cost involved in computation of the new procedures in this paper is negligible, its convergence rate is very fast and it implements effectively, so rather high accuracy of the derivative may be obtained on a unrefined meshes. Then it may be generally applied in engineering.We note that it is the first time that the O(h6) cionvergence of the derivative at nodes is achieved by this technique for bicubic finite element, which is proved in the third chapter.