For rectangular finite element, we give a superconvergence method by SPR technique based on the generalization of a new ultraconvergence record and the sharp Green function estimates, by which we prove that the deriva...For rectangular finite element, we give a superconvergence method by SPR technique based on the generalization of a new ultraconvergence record and the sharp Green function estimates, by which we prove that the derivative has ultra-convergence of order O(hk+3) (k 3 being odd) and displacement has order of O(hk+4) (k 4 being even) at the locally symmetry points.展开更多
A fully discrete discontinuous Galerkin method is introduced for solving time-dependent Maxwell’s equations.Distinguished from the Runge-Kutta discontinuous Galerkin method(RKDG)and the finite element time domain met...A fully discrete discontinuous Galerkin method is introduced for solving time-dependent Maxwell’s equations.Distinguished from the Runge-Kutta discontinuous Galerkin method(RKDG)and the finite element time domain method(FETD),in our scheme,discontinuous Galerkinmethods are used to discretize not only the spatial domain but also the temporal domain.The proposed numerical scheme is proved to be unconditionally stable,and a convergent rate O((△t)^(r+1)+h^(k+1/2))is established under the L^(2)-normwhen polynomials of degree atmost r and k are used for temporal and spatial approximation,respectively.Numerical results in both 2-D and 3-D are provided to validate the theoretical prediction.An ultra-convergence of order(△t)^(2r+1) in time step is observed numerically for the numerical fluxes w.r.t.temporal variable at the grid points.展开更多
文摘For rectangular finite element, we give a superconvergence method by SPR technique based on the generalization of a new ultraconvergence record and the sharp Green function estimates, by which we prove that the derivative has ultra-convergence of order O(hk+3) (k 3 being odd) and displacement has order of O(hk+4) (k 4 being even) at the locally symmetry points.
基金supported by the NSFC(11171104 and 10871066)the Science and Technology Grant of Guizhou Province(LKS[2010]05)+2 种基金supported by the NSFC(11171104 and 10871066)Hunan Provincial Innovation Foundation for Postgraduate(#CX2010B211).supported by the US National Science Foundation through grant DMS-1115530the Ministry of Education of China through the Changjiang Scholars program,the Guangdong Provincial Government of China through the”Computational Science Innovative Research Team”program,and Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University.
文摘A fully discrete discontinuous Galerkin method is introduced for solving time-dependent Maxwell’s equations.Distinguished from the Runge-Kutta discontinuous Galerkin method(RKDG)and the finite element time domain method(FETD),in our scheme,discontinuous Galerkinmethods are used to discretize not only the spatial domain but also the temporal domain.The proposed numerical scheme is proved to be unconditionally stable,and a convergent rate O((△t)^(r+1)+h^(k+1/2))is established under the L^(2)-normwhen polynomials of degree atmost r and k are used for temporal and spatial approximation,respectively.Numerical results in both 2-D and 3-D are provided to validate the theoretical prediction.An ultra-convergence of order(△t)^(2r+1) in time step is observed numerically for the numerical fluxes w.r.t.temporal variable at the grid points.
