This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
A modification of a finite element method of Douglas and Roberts for approximating the solution of the equations describing compressible miscible displacement in a porous medium is proposed and analyzed. The pressure ...A modification of a finite element method of Douglas and Roberts for approximating the solution of the equations describing compressible miscible displacement in a porous medium is proposed and analyzed. The pressure is treated by a parabolic mixed finite element method using a Raviart-Thomas space of index rover a quasiregular partition, An extension of the Darcy velocity along Gauss lines is used in the evaluation of the coefficients in the Galerkin procedure for the concentration. A simple computational procedure allows the superconvergence property of the fluid velocity to be retained in our total algorithm.展开更多
This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorit...This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorithm and their corresponding iterated correction schemes for this kind of equations.The superconvergemceof the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammersteinintegral equations generalized to nonlinear Fredilolm equations of the second kind, but also more precise resultsare obtained by tising the wavelet method.展开更多
The East Asian geological setting has a long duration related to the superconvergence of the Paleo-Asian, Tethyan and Paleo-Pacific tectonic domains. The Triassic Indosinian Movement contributed to an unified passive ...The East Asian geological setting has a long duration related to the superconvergence of the Paleo-Asian, Tethyan and Paleo-Pacific tectonic domains. The Triassic Indosinian Movement contributed to an unified passive continental margin in East Asia. The later ophiolites and I-type granites associated with subduction of the Paleo-Pacific Plate in the Late Triassic, suggest a transition from passive to active continental margins. With the presence of the ongoing westward migration of the Paleo-Pacific Subduction Zone, the sinistral transpressional stress field could play an important role in the intraplate deformation in East Asia during the Late Triassic to Middle Jurassic, being characterized by the transition from the E-W-trending structural system controlled by the Tethys and Paleo-Asian oceans to the NE-trending structural system caused by the Paleo-Pacific Ocean subduction. The continuously westward migration of the subduction zones resulted in the transpressional stress field in East Asia marked by the emergence of the Eastern North China Plateau and the formation of the Andean-type active continental margin from late Late Jurassic to Early Cretaceous （160-135 Ma）, accompanied by the development of a small amount of adakites. In the Late Cretaceous （135-90 Ma）, due to the eastward retreat of the Paleo-Pacific Subduction Zone, the regional stress field was replaced from sinistral transpression to transtension. Since a large amount of late-stage adakites and metamorphic core complexes developed, the Andean-type active continental margin was destroyed and the Eastern North China Plateau started to collapse. In the Late Cretaceous, the extension in East Asia gradually decreased the eastward retreat of the Paleo-Pacific subduction zones. Futhermore, a significant topographic inversion had taken place during the Cenozoic that resulted from a rapid uplift of the Tibet Plateau resulting from the India-Eurasian collision and the formation of the Bohai Bay Basin and other basins in the East Asian continental margin. The inversion caused a remarkable eastward migration of deformation, basin formation and magmatism. Meanwhile, the basins that mainly developed in the Paleogene resulted in a three-step topography which typically appears to drop eastward in altitude. In the Neogene, the basins underwent a rapid subsidence in some depressions after basin-controlled faulting, as well as the intracontinental extensional events in East Asia, and are likely to be a contribution to the uplift of the Tibetan Plateau.展开更多
The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain...The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis.展开更多
A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the v...A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.展开更多
Superconvergence has been studied for long, and many different numerical methods have been analyzed. This paper is concerned with the problem of superconvergence for a two-dimensional time-dependent linear Schr?dinger...Superconvergence has been studied for long, and many different numerical methods have been analyzed. This paper is concerned with the problem of superconvergence for a two-dimensional time-dependent linear Schr?dinger equation with the finite element method. The error estimate and superconvergence property with order O(hk+1)in the H1norm are given by using the elliptic projection operator in the semi-discrete scheme. The global superconvergence is derived by the interpolation post-processing technique. The superconvergence result with order O(hk+1+ τ2) in the H1norm can be obtained in the Crank-Nicolson fully discrete scheme.展开更多
An efficient time stepping procedure is proposed to treat the system describing compressible miscible displacement in a porous medium by employing a mixed finite element method to approximate the pressure and the flui...An efficient time stepping procedure is proposed to treat the system describing compressible miscible displacement in a porous medium by employing a mixed finite element method to approximate the pressure and the fluid velocity and a standard Galerkin method to approximate the concentration. An extension of the Darcy velocity along Gauss lines is used in the evaluation of the coefficients in the Galerkin procedure for the concentration. These results show that the total algorithm has the superconvergence property of the fluid velocity.展开更多
Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that fo...Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.展开更多
The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. ...The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpo- lation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis.展开更多
In this paper,we apply the Fourier analysis technique to investigate superconvergence properties of the direct disontinuous Galerkin(DDG)method(Liu and Yan in SIAM J Numer Anal 47(1):475-698,2009),the DDG method with ...In this paper,we apply the Fourier analysis technique to investigate superconvergence properties of the direct disontinuous Galerkin(DDG)method(Liu and Yan in SIAM J Numer Anal 47(1):475-698,2009),the DDG method with the interface correction(DDGIC)(Liu and Yan in Commun Comput Phys 8(3):541-564,2010),the symmetric DDG method(Vidden and Yan in Comput Math 31(6):638-662,2013),and the nonsymmetric DDG method(Yan in J Sci Comput 54(2):663-683,2013).We also include the study of the interior penalty DG(IPDG)method,due to its close relation to DDG methods.Error estimates are carried out for both P2 and P3 polynomial approximations.By investigating the quantitative errors at the Lobatto points,we show that the DDGIC and symmetric DDG methods are superior,in the sense of obtaining(k+2)th superconvergence orders for both P2 and P3 approximations.Superconvergence order of(k+2)is also observed for the IPDG method with P3 polynomial approximations.The errors are sensitive to the choice of the numerical flux coefficient for even degree P2 approximations,but are not for odd degree P3 approxi-mations.Numerical experiments are carried out at the same time and the numerical errors match well with the analytically estimated errors.展开更多
This paper discusses the semidiscrete finite element method for nonlinear hyperbolic equations with nonlinear boundary condition. The superclose property is derived through interpolation instead of the nonlinear H^1 p...This paper discusses the semidiscrete finite element method for nonlinear hyperbolic equations with nonlinear boundary condition. The superclose property is derived through interpolation instead of the nonlinear H^1 projection and integral identity technique. Meanwhile, the global superconvergence is obtained based on the interpolated postprocessing techniques.展开更多
One of the beneficial properties of the discontinuous Galerkin method is the accurate wave propagation properties.That is,the semi-discrete error has dissipation errors of order 2k+1(≤Ch2k+1)and order 2k+2 for disper...One of the beneficial properties of the discontinuous Galerkin method is the accurate wave propagation properties.That is,the semi-discrete error has dissipation errors of order 2k+1(≤Ch2k+1)and order 2k+2 for dispersion(≤Ch2k+2).Previous studies have concentrated on the order of accuracy,and neglected the important role that the error constant,C,plays in these estimates.In this article,we show the important role of the error constant in the dispersion and dissipation error for discontinuous Galerkin approximation of polynomial degree k,where k=0,1,2,3.This gives insight into why one may want a more centred flux for a piecewise constant or quadratic approximation than for a piecewise linear or cubic approximation.We provide an explicit formula for these error constants.This is illustrated through one particular flux,the upwind-biased flux introduced by Meng et al.,as it is a convex combination of the upwind and downwind fluxes.The studies of wave propagation are typically done through a Fourier ansatz.This higher order Fourier information can be extracted using the smoothness-increasing accuracy-conserving(SIAC)filter.The SIAC filter ties the higher order Fourier information to the negative-order norm in physical space.We show that both the proofs of the ability of the SIAC filter to extract extra accuracy and numerical results are unaffected by the choice of flux.展开更多
The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier...The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables.展开更多
In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges t...In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges to a particular projection of the exact solution.The order of this superconvergence is proved to be k+2 when piecewise Pk polynomials with K≥1 are used.The proof is valid for arbitrary non-uniform regular meshes and for piecewise polynomials with arbitrary K≥1.Furthermore,we find that the derivative and function value approxi?mations of the DG solution are superconvergent at a class of special points,with an order of k+1 and R+2,respectively.We also prove,under suitable choice of initial discretization,a(2k+l)-th order superconvergence rate of the DG solution for the numerical fluxes and the cell averages.Numerical experiments are given to demonstrate these theoretical results.展开更多
In this paper,we shall establish the superconvergence properties of the Runge-Kutta dis-continuous Galerkin method for solving two-dimensional linear constant hyperbolic equa-tion,where the upwind-biased numerical flu...In this paper,we shall establish the superconvergence properties of the Runge-Kutta dis-continuous Galerkin method for solving two-dimensional linear constant hyperbolic equa-tion,where the upwind-biased numerical flux is used.By suitably defining the correction function and deeply understanding the mechanisms when the spatial derivatives and the correction manipulations are carried out along the same or different directions,we obtain the superconvergence results on the node averages,the numerical fluxes,the cell averages,the solution and the spatial derivatives.The superconvergence properties in space are pre-served as the semi-discrete method,and time discretization solely produces an optimal order error in time.Some numerical experiments also are given.展开更多
Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金Supported by China State Major Rey Project for Basic Researches
文摘A modification of a finite element method of Douglas and Roberts for approximating the solution of the equations describing compressible miscible displacement in a porous medium is proposed and analyzed. The pressure is treated by a parabolic mixed finite element method using a Raviart-Thomas space of index rover a quasiregular partition, An extension of the Darcy velocity along Gauss lines is used in the evaluation of the coefficients in the Galerkin procedure for the concentration. A simple computational procedure allows the superconvergence property of the fluid velocity to be retained in our total algorithm.
文摘This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorithm and their corresponding iterated correction schemes for this kind of equations.The superconvergemceof the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammersteinintegral equations generalized to nonlinear Fredilolm equations of the second kind, but also more precise resultsare obtained by tising the wavelet method.
基金the financial supports received from the National Key Research and Development Program of China (Grants 2017YFC0601401 and 2016YFC0601002)National Natural Science Foundation of China (Grant Nos. 41325009, U1606401)+2 种基金National Science and Technology Major Project (Grant 2016ZX05004001003)National Ocean Bureau Program (GASI-GEOGE-1)the financial supports of Aoshan Elite Scientist Plan (2015ASTP-0S10) of Qingdao National Laboratory for Marine Science and Technology to Prof
文摘The East Asian geological setting has a long duration related to the superconvergence of the Paleo-Asian, Tethyan and Paleo-Pacific tectonic domains. The Triassic Indosinian Movement contributed to an unified passive continental margin in East Asia. The later ophiolites and I-type granites associated with subduction of the Paleo-Pacific Plate in the Late Triassic, suggest a transition from passive to active continental margins. With the presence of the ongoing westward migration of the Paleo-Pacific Subduction Zone, the sinistral transpressional stress field could play an important role in the intraplate deformation in East Asia during the Late Triassic to Middle Jurassic, being characterized by the transition from the E-W-trending structural system controlled by the Tethys and Paleo-Asian oceans to the NE-trending structural system caused by the Paleo-Pacific Ocean subduction. The continuously westward migration of the subduction zones resulted in the transpressional stress field in East Asia marked by the emergence of the Eastern North China Plateau and the formation of the Andean-type active continental margin from late Late Jurassic to Early Cretaceous （160-135 Ma）, accompanied by the development of a small amount of adakites. In the Late Cretaceous （135-90 Ma）, due to the eastward retreat of the Paleo-Pacific Subduction Zone, the regional stress field was replaced from sinistral transpression to transtension. Since a large amount of late-stage adakites and metamorphic core complexes developed, the Andean-type active continental margin was destroyed and the Eastern North China Plateau started to collapse. In the Late Cretaceous, the extension in East Asia gradually decreased the eastward retreat of the Paleo-Pacific subduction zones. Futhermore, a significant topographic inversion had taken place during the Cenozoic that resulted from a rapid uplift of the Tibet Plateau resulting from the India-Eurasian collision and the formation of the Bohai Bay Basin and other basins in the East Asian continental margin. The inversion caused a remarkable eastward migration of deformation, basin formation and magmatism. Meanwhile, the basins that mainly developed in the Paleogene resulted in a three-step topography which typically appears to drop eastward in altitude. In the Neogene, the basins underwent a rapid subsidence in some depressions after basin-controlled faulting, as well as the intracontinental extensional events in East Asia, and are likely to be a contribution to the uplift of the Tibetan Plateau.
基金Project supported by the National Natural Science Foundation of China (No. 10371113)
文摘The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis.
基金supported by the National Natural Science Foundation of China (Nos. 10971203 and 11271340)the Research Fund for the Doctoral Program of Higher Education of China (No. 20094101110006)
文摘A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.
基金Project supported by the National Natural Science Foundation of China(No.11671157)
文摘Superconvergence has been studied for long, and many different numerical methods have been analyzed. This paper is concerned with the problem of superconvergence for a two-dimensional time-dependent linear Schr?dinger equation with the finite element method. The error estimate and superconvergence property with order O(hk+1)in the H1norm are given by using the elliptic projection operator in the semi-discrete scheme. The global superconvergence is derived by the interpolation post-processing technique. The superconvergence result with order O(hk+1+ τ2) in the H1norm can be obtained in the Crank-Nicolson fully discrete scheme.
文摘An efficient time stepping procedure is proposed to treat the system describing compressible miscible displacement in a porous medium by employing a mixed finite element method to approximate the pressure and the fluid velocity and a standard Galerkin method to approximate the concentration. An extension of the Darcy velocity along Gauss lines is used in the evaluation of the coefficients in the Galerkin procedure for the concentration. These results show that the total algorithm has the superconvergence property of the fluid velocity.
基金This work is supported by the Foundatiorl of Zhongshan University Advanced Research Centre
文摘Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.
基金Project supported by the National Natural Science Foundation of China(Nos.10371113,10471133 and 10590353)
文摘The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpo- lation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis.
基金the National Science Foundation grant DMS-1620335 and Simons Foundation Grant 637716Research work of Xinghui Zhong is supported by the National Natural Science Foundation of China(NSFC)(Grant no.11871428).
文摘In this paper,we apply the Fourier analysis technique to investigate superconvergence properties of the direct disontinuous Galerkin(DDG)method(Liu and Yan in SIAM J Numer Anal 47(1):475-698,2009),the DDG method with the interface correction(DDGIC)(Liu and Yan in Commun Comput Phys 8(3):541-564,2010),the symmetric DDG method(Vidden and Yan in Comput Math 31(6):638-662,2013),and the nonsymmetric DDG method(Yan in J Sci Comput 54(2):663-683,2013).We also include the study of the interior penalty DG(IPDG)method,due to its close relation to DDG methods.Error estimates are carried out for both P2 and P3 polynomial approximations.By investigating the quantitative errors at the Lobatto points,we show that the DDGIC and symmetric DDG methods are superior,in the sense of obtaining(k+2)th superconvergence orders for both P2 and P3 approximations.Superconvergence order of(k+2)is also observed for the IPDG method with P3 polynomial approximations.The errors are sensitive to the choice of the numerical flux coefficient for even degree P2 approximations,but are not for odd degree P3 approxi-mations.Numerical experiments are carried out at the same time and the numerical errors match well with the analytically estimated errors.
基金Supported by the National Natural Science Foundation of China (10671184)
文摘This paper discusses the semidiscrete finite element method for nonlinear hyperbolic equations with nonlinear boundary condition. The superclose property is derived through interpolation instead of the nonlinear H^1 projection and integral identity technique. Meanwhile, the global superconvergence is obtained based on the interpolated postprocessing techniques.
基金This work was sponsored by the Air Force Office of Scientific Research(AFOSR),Air Force Material Command,USAF,under grant number FA8655-09-1-3017
文摘One of the beneficial properties of the discontinuous Galerkin method is the accurate wave propagation properties.That is,the semi-discrete error has dissipation errors of order 2k+1(≤Ch2k+1)and order 2k+2 for dispersion(≤Ch2k+2).Previous studies have concentrated on the order of accuracy,and neglected the important role that the error constant,C,plays in these estimates.In this article,we show the important role of the error constant in the dispersion and dissipation error for discontinuous Galerkin approximation of polynomial degree k,where k=0,1,2,3.This gives insight into why one may want a more centred flux for a piecewise constant or quadratic approximation than for a piecewise linear or cubic approximation.We provide an explicit formula for these error constants.This is illustrated through one particular flux,the upwind-biased flux introduced by Meng et al.,as it is a convex combination of the upwind and downwind fluxes.The studies of wave propagation are typically done through a Fourier ansatz.This higher order Fourier information can be extracted using the smoothness-increasing accuracy-conserving(SIAC)filter.The SIAC filter ties the higher order Fourier information to the negative-order norm in physical space.We show that both the proofs of the ability of the SIAC filter to extract extra accuracy and numerical results are unaffected by the choice of flux.
基金The NNSF (99200204) of Liaoning Province, China.
文摘The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables.
文摘In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges to a particular projection of the exact solution.The order of this superconvergence is proved to be k+2 when piecewise Pk polynomials with K≥1 are used.The proof is valid for arbitrary non-uniform regular meshes and for piecewise polynomials with arbitrary K≥1.Furthermore,we find that the derivative and function value approxi?mations of the DG solution are superconvergent at a class of special points,with an order of k+1 and R+2,respectively.We also prove,under suitable choice of initial discretization,a(2k+l)-th order superconvergence rate of the DG solution for the numerical fluxes and the cell averages.Numerical experiments are given to demonstrate these theoretical results.
基金Yuan Xu is supported by the NSFC Grant 11671199Qiang Zhang is supported by the NSFC Grant 11671199.
文摘In this paper,we shall establish the superconvergence properties of the Runge-Kutta dis-continuous Galerkin method for solving two-dimensional linear constant hyperbolic equa-tion,where the upwind-biased numerical flux is used.By suitably defining the correction function and deeply understanding the mechanisms when the spatial derivatives and the correction manipulations are carried out along the same or different directions,we obtain the superconvergence results on the node averages,the numerical fluxes,the cell averages,the solution and the spatial derivatives.The superconvergence properties in space are pre-served as the semi-discrete method,and time discretization solely produces an optimal order error in time.Some numerical experiments also are given.
文摘Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
