Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
In this paper, by using the Lp-Brunn-Minkowski theory and its dual theory, L2-version on the conjectured projection inequality is investigated, the （reverse） inclusive relationship between L2-projection body and the...In this paper, by using the Lp-Brunn-Minkowski theory and its dual theory, L2-version on the conjectured projection inequality is investigated, the （reverse） inclusive relationship between L2-projection body and the classical projection body are established, and a constrained minimization problem is solved.展开更多
We develop an efficient one-dimensional moving mesh algorithm for solving partial differential equations.The main contribution of this paper is to design an effective interpolation scheme based on L2-projection for th...We develop an efficient one-dimensional moving mesh algorithm for solving partial differential equations.The main contribution of this paper is to design an effective interpolation scheme based on L2-projection for the moving mesh method.The proposed method preserves not only the mass-conservation but also the first order momentum of the underlying numerical solution at each mesh redistribution step.Numerical examples are presented to demonstrate the effectiveness of the new interpolation technique.展开更多
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
文摘Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
基金supported by the National Natural Sciences Foundation of China (Grant Nos.10671117,10801140)
文摘In this paper, by using the Lp-Brunn-Minkowski theory and its dual theory, L2-version on the conjectured projection inequality is investigated, the （reverse） inclusive relationship between L2-projection body and the classical projection body are established, and a constrained minimization problem is solved.
文摘We develop an efficient one-dimensional moving mesh algorithm for solving partial differential equations.The main contribution of this paper is to design an effective interpolation scheme based on L2-projection for the moving mesh method.The proposed method preserves not only the mass-conservation but also the first order momentum of the underlying numerical solution at each mesh redistribution step.Numerical examples are presented to demonstrate the effectiveness of the new interpolation technique.
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）.
