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| 1 | An hp Adaptive Uniaxial Perfectly Matched Layer Method for Helmholtz Scattering Problems显示文摘We propose an adaptive strategy for solving high frequency Helmholtz scattering problems.The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into the bounded domain.The parameters in the uniaxial PML method are determined by sharp a posteriori error estimates developed by Chen and Wu[8].An hp-adaptive finite element strategy is proposed to solve the uniaxial PML equation.Numerical experiments are included which indicate the desirable exponential decay property of the error. | Zhiming Chen Benqi Guo Yuanming Xiao | 2009 | Communications in Computational Physics2009，5，2： | 1 |
| 2 | An h-p Petrov-Galerkin finite element method for linear Volterra integro-differential equations显示文摘We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover,we observe that the numerical scheme superconverges at the nodal points of the time partition. | YI LiJun GUO BenQi | 2014 | Science China Mathematics2014，57，11： | 1 |
| 3 | Preface显示文摘This is a focused issue dedicated to the memory of the late Professor Ben-yu Guo(1942-2016),a prominent numerical analyst at Shanghai University and Shanghai Normal University,and a prolific researcher with more than 300 peer-reviewed publications,many of which are in prestigious journals.His work has been well recognized in the world and extensively cited.He received numerous prestigious awards,including a degree of Doctor of Science honoris causa from Sanford University in England. | Benqi Guo Heping Ma Jie Shen Chi-Wang Shu Li-Lian Wang | 2019 | Communications on Applied Mathematics and Computation2019，1，1： | 0 |
| 4 | A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension显示文摘In this paper,a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems.The key idea is to postprocess the Galerkin approximation,and the analysis shows that the postprocess improves the order of convergence.Consequently,we obtain asymptotically exact aposteriori error estimators based on the postprocessing results.Numerical examples are included to illustrate the theoretical analysis. | Lijun Yi Benqi Guo | 2010 | Numerical Mathematics(Theory,Methods and Applications)2010，3，1： | 0 |
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