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...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.展开更多
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 ...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.展开更多
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 ...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.展开更多
基金supported partially by the innovation fund of Shanghai Normal Universitysupported partially by NSERC of Canada under Grant OGP0046726.
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.
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.
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.
