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A NONLINEAR GALERKIN MIXED ELEMENT METHOD AND A POSTERIORI ERROR ESTIMATOR FOR THE STATIONARY NAVIER-STOKES EQUATIONS
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作者 罗振东 朱江 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第10期1194-1206,共13页
A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution... A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived. 展开更多
关键词 Navier-Stokes equation nonlinear Galerkin mixed element method error estimate posteriori error estimator
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An Anisotropic Posteriori Error Estimator of Bilinear Element
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作者 YIN Li ZHI Gui-zhen 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第4期492-499,共8页
The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel a... The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel approaches and techniques, the optimal error estimates and some superconvergence results axe obtained without the regulaxity assumption and quasi-uniform assumption requirements on the meshes. Then, based on these results, we give an anisotropic posteriori error estimate for the second problem. 展开更多
关键词 finite element method ANISOTROPIC SUPERCONVERGENCE posteriori error estimate
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THE A POSTERIORI ERROR ESTIMATOR OF SDG METHOD FOR VARIABLE COEFFICIENTS TIME-HARMONIC MAXWELL'S EQUATIONS
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作者 Wei Yang Xin Liu +1 位作者 Bin He Yunqing Huang 《Journal of Computational Mathematics》 SCIE CSCD 2023年第2期263-286,共24页
In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's equations.We propose two a posteriori error estimators,one is the recovery-type estimator,and... In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's equations.We propose two a posteriori error estimators,one is the recovery-type estimator,and the other is the residual-type estimator.We first propose the curl-recovery method for the staggered discontinuous Galerkin method(SDGM),and based on the super-convergence result of the postprocessed solution,an asymptotically exact error estimator is constructed.The residual-type a posteriori error estimator is also proposed,and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's equations.The efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments. 展开更多
关键词 Maxwell’s equations A posteriori error estimation Staggered discontinuous Galerkin
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ON RESIDUAL-BASED A POSTERIORI ERROR ESTIMATORS FOR LOWEST-ORDER RAVIART-THOMAS ELEMENT APPROXIMATION TO CONVECTION-DIFFUSION-REACTION EQUATIONS 被引量:2
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作者 Shaohong Du Xiaoping Xie 《Journal of Computational Mathematics》 SCIE CSCD 2014年第5期522-546,共25页
A new technique of residual-type a posteriori error analysis is developed for the lowest- order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension... A new technique of residual-type a posteriori error analysis is developed for the lowest- order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed scheme and upwind-weighted mixed scheme are considered. The a posteriori error estimators, derived for the stress variable error plus scalar displacement error in L_2-norm, can be directly computed with the solutions of the mixed schemes without any additional cost, and are proven to be reliable. Local efficiency dependent on local variations in coefficients is obtained without any saturation assumption, and holds from the cases where convection or reaction is not present to convection- or reaction-dominated problems. The main tools of the analysis are the postprocessed approximation of scalar displacement, abstract error estimates, and the property of modified Oswald interpolation. Numerical experiments are carried out to support our theoretical results and to show the competitive behavior of the proposed posteriori error estimates. 展开更多
关键词 Convection-diffusion-reaction equation Centered mixed scheme Upwind-weightedmixed scheme Postproeessed approximation A posteriori error estimators.
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An accurate a posteriori error estimator for the Steklov eigenvalue problem and its applications
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作者 Fei Xu Qiumei Huang 《Science China Mathematics》 SCIE CSCD 2021年第3期623-638,共16页
In this paper, a type of accurate a posteriori error estimator is proposed for the Steklov eigenvalue problem based on the complementary approach, which provides an asymptotic exact estimate for the approximate eigenp... In this paper, a type of accurate a posteriori error estimator is proposed for the Steklov eigenvalue problem based on the complementary approach, which provides an asymptotic exact estimate for the approximate eigenpair. Besides, we design a type of cascadic adaptive finite element method for the Steklov eigenvalue problem based on the proposed a posteriori error estimator. In this new cascadic adaptive scheme, instead of solving the Steklov eigenvalue problem in each adaptive space directly, we only need to do some smoothing steps for linearized boundary value problems on a series of adaptive spaces and solve some Steklov eigenvalue problems on a low dimensional space. Furthermore, the proposed a posteriori error estimator provides the way to refine meshes and control the number of smoothing steps for the cascadic adaptive method. Some numerical examples are presented to validate the efficiency of the algorithm in this paper. 展开更多
关键词 Steklov eigenvalue problem a posteriori error estimator cascadic multigrid method adaptive finite element method complementary method
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A TYPE OF NEW POSTERIORI ERROR ESTIMATORS FOR STOKES PROBLEMS
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作者 罗振东 王烈衡 李雅如 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2001年第2期173-182,共10页
In this paper, a new discrete formulation and a type of new posteriori error estimators for the second-order element discretization for Stokes problems are presented, where pressure is approximated with piecewise fir... In this paper, a new discrete formulation and a type of new posteriori error estimators for the second-order element discretization for Stokes problems are presented, where pressure is approximated with piecewise first-degree polynomials and velocity vector field with piecewise second-degree polynomials with a cubic bubble function to be added. The estimators are the globally upper and locally lower bounds for the error of the finite element discretization. It is shown that the bubble part for this second-order element approximation is substituted for the other parts of the approximate solution. 展开更多
关键词 Stokes problems posteriori error estimators the second-order element
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A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations
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作者 Yiming Wen Luoping Chen Jiajia Dai 《Journal of Applied Mathematics and Physics》 2023年第2期361-376,共16页
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m... In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator. 展开更多
关键词 Two-Grid Mixed Finite Element Methods posteriori error Estimates Semilinear Elliptic Equations Averaging Technique
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A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation 被引量:5
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作者 Ningning Yan Zhaojie Zhou 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第3期297-320,共24页
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc... In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results. 展开更多
关键词 Constrained optimal control problem convection dominated diffusion equation stream-line diffusion finite element method a priori error estimate a posteriori error estimate.
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AN ASYMPTOTIC BEHAVIOR AND A POSTERIORI ERROR ESTIMATES FOR THE GENERALIZED SCHWARTZ METHOD OF ADVECTION-DIFFUSION EQUATION
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作者 Salah BOULAARAS Mohammed Said TOUATI BRAHIM +1 位作者 Smail BOUZENADA Abderrahmane ZARAI 《Acta Mathematica Scientia》 SCIE CSCD 2018年第4期1227-1244,共18页
In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are prove... In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method. Furthermore, an asymptotic behavior in Sobolev norm is de- duced using Benssoussau-Lions' algorithm. Finally, the results of some numerical experiments are presented to support the theory. 展开更多
关键词 a posteriori error estimates GODDM ADVECTION-DIFFUSION Galerkin method Benssoussan-Lions' algorithm
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RESIDUAL A POSTERIORI ERROR ESTIMATE TWO-GRID METHODS FOR THE STEADY (NAVIER-STOKES) EQUATION WITH STREAM FUNCTION FORM
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作者 任春风 马逸尘 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第5期546-559,共14页
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met... Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution. 展开更多
关键词 two-level method Navier-Stokes equation residual a posteriori error estimate finite element method stream function form
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Residual-type a posteriori error estimate for parabolic obstacle problems
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作者 李京梁 马和平 《Journal of Shanghai University(English Edition)》 CAS 2006年第6期473-478,共6页
In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator wh... In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained. 展开更多
关键词 finite element approximations variational inequalities parabolic obstacle problems a posteriori error estimates.
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A POSTERIORI ERROR ESTIMATE OF THE DSD METHOD FOR FIRST-ORDER HYPERBOLIC EQUATIONS
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作者 KANG Tong(康彤) +1 位作者 YU De-hao(余德浩) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第6期732-740,共9页
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illus... A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method. 展开更多
关键词 posteriori error estimate discontinuous-streamline diffusion method first-order hyperbolic equation
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A Posteriori Error Estimates for Finite Element Methods for Systems of Nonlinear,Dispersive Equations
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作者 Ohannes A.Karakashian Michael M.Wise 《Communications on Applied Mathematics and Computation》 2022年第3期823-854,共32页
The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite ... The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes.In this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin methods.We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators. 展开更多
关键词 Finite element methods Discontinuous Galerkin methods Korteweg-de Vries equation A posteriori error estimates Conservation laws Nonlinear equations Dispersive equations
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A Posteriori Error Estimate of Weak Galerkin FEM for Stokes Problem Using Auxiliary Subspace Techniques
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作者 Jiachuan Zhang Ran Zhang Xiaoshen Wang 《Communications in Computational Physics》 SCIE 2023年第2期511-537,共27页
Based on the auxiliary subspace techniques,a posteriori error estimator of nonconforming weak Galerkin finite element method(WGFEM)for Stokes problem in two and three dimensions is presented.Without saturation assumpt... Based on the auxiliary subspace techniques,a posteriori error estimator of nonconforming weak Galerkin finite element method(WGFEM)for Stokes problem in two and three dimensions is presented.Without saturation assumption,we prove that the WGFEM approximation error is bounded by the error estimator up to an oscillation term.The computational cost of the approximation and the error problems is considered in terms of size and sparsity of the system matrix.To reduce the computational cost of the error problem,an equivalent error problem is constructed by using diagonalization techniques,which needs to solve only two diagonal linear algebraic systems corresponding to the degree of freedom(d.o.f)to get the error estimator.Numerical experiments are provided to demonstrate the effectiveness and robustness of the a posteriori error estimator. 展开更多
关键词 Auxiliary subspace techniques diagonalization techniques weak Galerkin A posteriori error estimate Stokes problem.
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Residual-based a posteriori error estimates of nonconforming finite element method for elliptic problems with Dirac delta source terms 被引量:4
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作者 DU ShaoHong XIE XiaoPing 《Science China Mathematics》 SCIE 2008年第8期1440-1460,共21页
Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which ... Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which yields global upper and lower bounds for the error in piecewise W1,p seminorm.The other one is proved to give a global upper bound of the error in Lp-norm.By taking the two estimators as refinement indicators,adaptive algorithms are suggested,which are experimentally shown to attain optimal convergence orders. 展开更多
关键词 Crouzeix-Raviart element nonconforming FEM a posteriori error estimator longest edge bisection 65N15 65N30 65N50
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A POSTERIORI ESTIMATOR OF NONCONFORMING FINITE ELEMENT METHOD FOR FOURTH ORDER ELLIPTIC PERTURBATION PROBLEMS 被引量:1
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作者 Shuo Zhang Ming Wang 《Journal of Computational Mathematics》 SCIE EI CSCD 2008年第4期554-577,共24页
In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an a posteriori error estimator under certain conditions, and giv... In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an a posteriori error estimator under certain conditions, and give an h-version adaptive algorithm based on the error estimation. The local behavior of the estimator is analyzed as well. This estimator works for several nonconforming methods, such as the modified Morley method and the modified Zienkiewicz method, and under some assumptions, it is an optimal one. Numerical examples are reported, with a linear stationary Cahn-HiUiard-type equation as a model problem. 展开更多
关键词 Fourth order elliptic perturbation problems Nonconforming finite elementmethod A posteriori error estimator Adaptive algorithm Local behavior.
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Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method 被引量:1
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作者 BAI YanHong WU YongKe XIE XiaoPing 《Science China Mathematics》 SCIE CSCD 2016年第9期1835-1850,共16页
Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of or... Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results. 展开更多
关键词 linear elasticity hybrid stress finite element superconvergence recovery a posteriori error estimator
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Residual-based a posteriori error estimates for symmetric conforming mixed finite elements for linear elasticity problems
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作者 Long Chen Jun Hu +1 位作者 Xuehai Huang Hongying Man 《Science China Mathematics》 SCIE CSCD 2018年第6期973-992,共20页
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are p... A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are proved. Numerical examples are presented to verify the theoretical results. 展开更多
关键词 symmetric mixed finite element linear elasticity problems a posteriori error estimator adaptivemethod
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UNIFORMLY A POSTERIORI ERROR ESTIMATE FOR THE FINITE ELEMENT METHOD TO A MODEL PARAMETER DEPENDENT PROBLEM
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作者 Yiran Zhang Jun Hu 《Journal of Computational Mathematics》 SCIE EI CSCD 2008年第5期716-727,共12页
This paper proposes a reliable and efficient a posteriori error estimator for the finite element methods for the beam problem. It is proved that the error can be bounded by the computable error estimator from above an... This paper proposes a reliable and efficient a posteriori error estimator for the finite element methods for the beam problem. It is proved that the error can be bounded by the computable error estimator from above and below up to multiplicative constants that do neither depend on the meshsize nor on the thickness of the beam. 展开更多
关键词 The beam problem A posteriori error estimator Finite element method.
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Posteriori Error Estimation for an Interior Penalty Discontinuous Galerkin Method for Maxwell’s Equations in Cold Plasma
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作者 Jichun Li 《Advances in Applied Mathematics and Mechanics》 SCIE 2009年第1期107-124,共18页
In this paper,we develop a residual-based a posteriori error estimator for the time-dependent Maxwell’s equations in the cold plasma.Here we consider a semi-discrete interior penalty discontinuous Galerkin(DG)method ... In this paper,we develop a residual-based a posteriori error estimator for the time-dependent Maxwell’s equations in the cold plasma.Here we consider a semi-discrete interior penalty discontinuous Galerkin(DG)method for solving the governing equations.We provide both the upper bound and lower bound analysis for the error estimator.This is the first posteriori error analysis carried out for the Maxwell’s equations in dispersive media. 展开更多
关键词 posteriori error estimator Maxwell’s equations cold plasma discontinuous Galerkin method
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