Consider L<sup>2</sup>-projection u<sub>h</sub> of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for const...Consider L<sup>2</sup>-projection u<sub>h</sub> of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for constructing a superclose to function u<sub>h</sub> are proposed and then superconvergence for both u<sub>h</sub> and Du<sub>h</sub> are proved. When n is odd and no boundary conditions are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order Gauss points G<sub>n+1</sub> in each element. When n is even and function values on the boundary are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order points Z<sub>n+1</sub> in each element. If the other boundary conditions are given, then the conclusions are valid in all elements that its distance from the boundary≥ch|lnh|. The above conclusions are also valid. for n-dergree rectangular element Q<sub>1</sub> （n）.展开更多
基金Supported by the National Natrual Science Funds of China
文摘Consider L<sup>2</sup>-projection u<sub>h</sub> of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for constructing a superclose to function u<sub>h</sub> are proposed and then superconvergence for both u<sub>h</sub> and Du<sub>h</sub> are proved. When n is odd and no boundary conditions are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order Gauss points G<sub>n+1</sub> in each element. When n is even and function values on the boundary are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order points Z<sub>n+1</sub> in each element. If the other boundary conditions are given, then the conclusions are valid in all elements that its distance from the boundary≥ch|lnh|. The above conclusions are also valid. for n-dergree rectangular element Q<sub>1</sub> （n）.
