We study the enhancement of accuracy,by means of the convolution postprocessing technique,for discontinuous Galerkin(DG)approximations to hyperbolic problems.Previous investigations have focused on the superconvergenc...We study the enhancement of accuracy,by means of the convolution postprocessing technique,for discontinuous Galerkin(DG)approximations to hyperbolic problems.Previous investigations have focused on the superconvergence obtained by this technique for elliptic,time-dependent hyperbolic and convection-diffusion problems.In this paper,we demonstrate that it is possible to extend this postprocessing technique to the hyperbolic problems written as the Friedrichs’systems by using an upwind-like DG method.We prove that the L2-error of the DG solution is of order k+1/2,and further the post-processed DG solution is of order 2k+1 if Qkpolynomials are used.The key element of our analysis is to derive the(2k+1)-order negative norm error estimate.Numerical experiments are provided to illustrate the theoretical analysis.展开更多
The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows： one is that the model has a stable periodic trajectory from Hopf ...The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows： one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an eco- logical balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results.展开更多
基金This work was supported by the State Key Laboratory of Synthetical Automation for Process Industries Fundamental Research Funds 2013ZCX02the National Natural Science Funds of China 11371081
文摘We study the enhancement of accuracy,by means of the convolution postprocessing technique,for discontinuous Galerkin(DG)approximations to hyperbolic problems.Previous investigations have focused on the superconvergence obtained by this technique for elliptic,time-dependent hyperbolic and convection-diffusion problems.In this paper,we demonstrate that it is possible to extend this postprocessing technique to the hyperbolic problems written as the Friedrichs’systems by using an upwind-like DG method.We prove that the L2-error of the DG solution is of order k+1/2,and further the post-processed DG solution is of order 2k+1 if Qkpolynomials are used.The key element of our analysis is to derive the(2k+1)-order negative norm error estimate.Numerical experiments are provided to illustrate the theoretical analysis.
基金Acknowledgments This work was supported by the Science Foundation of Liaoning Province （20092179） and by the National Natural Science Foundation （60974004/F030101）.
文摘The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows： one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an eco- logical balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results.
