This paper is concerned with the error behaviour of Runge-Kutta methods ap- plied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimate of algeb...This paper is concerned with the error behaviour of Runge-Kutta methods ap- plied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimate of algebraically and diagonally stable Runge-Kutta methods with Lagrange interpolation procedure. Numerical experiments confirm our theoretical analysis.展开更多
We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H（div）- conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocit...We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H（div）- conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H（div）-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.展开更多
This paper applies a difference scheme to a singularly perturbed problem. The authors provide two algorithms on moving mesh methods by using Richardson extrapolation which can improve the accuracy of numerical solutio...This paper applies a difference scheme to a singularly perturbed problem. The authors provide two algorithms on moving mesh methods by using Richardson extrapolation which can improve the accuracy of numerical solution. In traditional algorithms of moving meshes, the initial mesh is a uniform mesh. The authors change it to Bakhvalov-Shishkin mesh, and prove that it improves efficiency by numerical experiments. Finally, the results of the two algorithms are analyzed.展开更多
文摘This paper is concerned with the error behaviour of Runge-Kutta methods ap- plied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimate of algebraically and diagonally stable Runge-Kutta methods with Lagrange interpolation procedure. Numerical experiments confirm our theoretical analysis.
基金supported by National Natural Science Foundation of China(Grant No.11071226)the Hong Kong Research Grants Council(Grant No.201112)
文摘We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H（div）- conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H（div）-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.
基金This work is supported by the Foundation for Talent Introduction of Guangdong Provincial University, Guang- dong Province Universities and Colleges Pearl River Scholar Funded Scheme （2008）, and the National Natural Science Foundation of China under Grant No. 10971074.
文摘This paper applies a difference scheme to a singularly perturbed problem. The authors provide two algorithms on moving mesh methods by using Richardson extrapolation which can improve the accuracy of numerical solution. In traditional algorithms of moving meshes, the initial mesh is a uniform mesh. The authors change it to Bakhvalov-Shishkin mesh, and prove that it improves efficiency by numerical experiments. Finally, the results of the two algorithms are analyzed.
