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
This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the ...This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) fltering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of diferent resolutions. Although this article presents the details of the SIAC flter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.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This work was motivated by discussions with Dr.Venke Sankaran(Edwards Air Force Research Lab,USA)and was performed while visiting the Applied Mathematics group at HeinrichHeine University,Düsseldorf,Germany.Research supported by the Air Force Ofce of Scientifc Research(AFOSR)Computational Mathematics Program(Program Manager:Dr.Fariba Fahroo)under Grant numbers FA9550-18-1-0486 and FA9550-19-S-0003.
文摘This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) fltering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of diferent resolutions. Although this article presents the details of the SIAC flter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.
