The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the ...The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the explicit Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and the Gori-Micchelli weight.展开更多
In this paper, a biquartic finite volume element method based on Lobatto- Guass structure is presented for variable coefficient elliptic equation on rectangular partition. Not only the optimal H1 and L2 error estimate...In this paper, a biquartic finite volume element method based on Lobatto- Guass structure is presented for variable coefficient elliptic equation on rectangular partition. Not only the optimal H1 and L2 error estimates but also some superconvergent properties are available and could be proved for this method. The numerical results obtained by this finite volume element scheme confirm the validity of the theoretical analysis and the effectiveness of this method.展开更多
We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order ...We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.展开更多
文摘The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the explicit Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and the Gori-Micchelli weight.
文摘In this paper, a biquartic finite volume element method based on Lobatto- Guass structure is presented for variable coefficient elliptic equation on rectangular partition. Not only the optimal H1 and L2 error estimates but also some superconvergent properties are available and could be proved for this method. The numerical results obtained by this finite volume element scheme confirm the validity of the theoretical analysis and the effectiveness of this method.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171125, 11271118, 91130003）, the National Natural Science Foundation of China （Tianyuan Fund for Mathematics, Grant No. 11226170）, the Natural Science Foundation of Hunan Province （Grant No. 13JJ4095）, the Postdoctoral Foundation of China （Grant No. 20100471182）, the Construct Program of the Key Discipline in Hunan Province, and the Key Foundation of Hunan Provincial Education Department （Grant No. 11A043）.
文摘We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.
