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Error estimates of H^1-Galerkin mixed finite element method for Schrdinger equation 认领 引用 被引量：31
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作者 LIU Yang LI Hong WANG Jin-feng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2009年第1期83-89,共7页
An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same t... An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition. 展开更多
关键词 H1-Galerkin mixed finite element method Schrdinger equation LBB condition optimal error estimates
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MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅱ)——THE DISCRETE-TIME CASE ALONG CHARACTERISTICS 认领 引用 被引量：1
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作者 罗振东 朱江 +1 位作者 曾庆存 谢正辉 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第2期186-201,共16页
The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE s... The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete_time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated. 展开更多
关键词 mixed finite element method shallow water equation error estimate current and silt sedimentation characteristics method
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MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTA-TION (Ⅰ)-THE CONTINUOUS-TIME CASE 认领 引用
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作者 罗振东 朱江 +1 位作者 曾庆存 谢正辉 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第1期80-92,共13页
An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation, the equation of bottom topography change,and of some boundary and initial conditions is stu... An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation, the equation of bottom topography change,and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element(MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived.The error estimates are optimal. 展开更多
关键词 mixed finite element method shallow water equation error estimate current and silt sedimentation
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Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations 认领 引用
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作者 罗振东 周艳杰 朱江 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第5期665-675,共11页
The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing... The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas. 展开更多
关键词 vapor deposition chemical reaction equation the mixed finite element method semidiscrete formulation fully discrete formulation
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IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE 认领 引用
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作者 陈蔚 《Acta Mathematica Scientia》 SCIE 2003年第3期386-398,共13页
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equ... The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived. 展开更多
关键词 Semiconductor device strongly A(0)-stable multistep methods finite element methods mixed finite element methods
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Nonlinear simulation of arch dam cracking with mixed finite element method 认领 引用 被引量：1
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作者 Ren Hao Li Tongchun +1 位作者 Chen Huifang Zhao Lanhao 《Water Science and Engineering》 CAS 2008年第2期88-101,共14页
This paper proposes a new,simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period,which takes into account the arch dam construction process and t... This paper proposes a new,simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period,which takes into account the arch dam construction process and temperature loads.In the calculation mesh,the contact surface of pair nodes is located at places on the arch dam where cracking is possible.A new effective iterative method,the mixed finite element method for friction-contact problems,is improved and used for nonlinear simulation of the cracking process.The forces acting on the structure are divided into two parts:external forces and contact forces.The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable,so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical.This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China.In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking,three schemes were designed for calculation.Numerical results agree with actual measured data,proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking. 展开更多
关键词 mixed finite element method contact pair nodes crack of arch dam simulation thermal stress
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LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR A CLASS OF STOKES EQUATION 认领 引用
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作者 顾海明 羊丹平 +1 位作者 隋树林 刘新民 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第5期557-566,共10页
A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary ... A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces. 展开更多
关键词 least-squares mixed finite element method error estimates
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A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations 认领 引用 被引量：1
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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 Residual-free Bubbles-mixed Finite Element Method for Ellipticconvection-dominated Diffusion Problems 认领 引用
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《大学数学》 2013年第5期18-22,共5页
Abstract： Using the standard mixed finite element to model the convection-dominated diffusion problems, one can only get an unstable scheme which produces severely oscillating approximate solutions. To simultaneously... Abstract： Using the standard mixed finite element to model the convection-dominated diffusion problems, one can only get an unstable scheme which produces severely oscillating approximate solutions. To simultaneously achieve stability and accuracy, we present a new stabilized mixed finite element method for the elliptic problems, which called residual-free bubbles-mixed finite element method, and the existence and uniqueness o{ the discrete solution are proved. Finally optimal error estimate with e are derived. 展开更多
关键词 residual-free bubbles elliptic convection-dominated diffusion problems stabilized mixed finite element method
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Two Classes of Mixed Finite Element Methods for the Reissner-Mindlin Plate Problem 认领 引用
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作者 Jun Hu Xueqin Yang 《Communications on Applied Mathematics and Computation》 EI CSCD 2025年第3期1098-1121,共24页
In this paper,we propose mixed finite element methods for the Reissner-Mindlin Plate Problem by introducing the bending moment as an independent variable.We apply the finite element approximations of the stress field ... In this paper,we propose mixed finite element methods for the Reissner-Mindlin Plate Problem by introducing the bending moment as an independent variable.We apply the finite element approximations of the stress field and the displacement field constructed for the elasticity problem by Hu(J Comp Math 33:283–296,2015),Hu and Zhang(arXiv:1406.7457,2014)to solve the bending moment and the rotation for the Reissner-Mindlin Plate Problem.We propose two triples of finite element spaces to approximate the bending moment,the rotation,and the displacement.The feature of these methods is that they need neither reduction terms nor penalty terms.Then,we prove the well-posedness of the discrete problem and obtain the optimal estimates independent of the plate thickness.Finally,we present some numerical examples to demonstrate the theoretical results. 展开更多
关键词 Reissner-Mindlin plate Mixed finite element method Linear elasticity
Static and dynamic analyses of two-phase/multi-phase carbon nanotube-reinforced functionally graded composite beams via warping-included mixed finite element method 认领 引用
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作者 Merve ERMIS Umit N.ARIBAS +2 位作者 Emrah MANDENCI Emre KAHRAMAN Mehmet H.OMURTAG 《Frontiers of Structural and Civil Engineering》 SCIE EI CAS CSCD 2025年第6期980-1004,共25页
This study enhances the application of cross-sectional warping considered mixed finite element(WMFE)formulation to accurately determine natural vibration,static displacement response,and shear and normal stress evalua... This study enhances the application of cross-sectional warping considered mixed finite element(WMFE)formulation to accurately determine natural vibration,static displacement response,and shear and normal stress evaluation with very close to the precision of solid finite elements(FEs)in two-phase/multi-phase functionally graded(FG)laminated composite beams strength using carbon nanotubes(CNTs).The principles of three dimensional(3D)elasticity theory are used to derive constitutive equations.The mixed finite element(MFE)method is improved by accounting for warping effects by displacement-based FEs within the cross-sectional domain.The MFE with two nodes has a total of 24 degrees of freedom.The two-phase material consists of a polymer matrix reinforced with aligned CNTs that are FG throughout the beam thickness.The multi-phase FG beam is modeled as a three-component composite material,consisting of CNTs,a polymer matrix,and fibers.The polymer matrix is reinforced by longitudinally aligned fibers and randomly dispersed CNT particles.The fiber volume fractions are considered to change gradually through the thickness of the beam following a power-law variation.The W-MFE achieves satisfactory results with fewer degrees of freedom than 3D solid FEs.Benchmark examples examine the effects of ply orientation,configuration,and fiber gradation on FG beam behavior. 展开更多
关键词 stress analysis natural vibration analysis CNT-reinforced composites mixed finite element method functionally graded material
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A WEAK GALERKIN MIXED FINITE ELEMENT METHOD FOR LINEAR ELASTICITY WITHOUT ENFORCED SYMMETRY 认领 引用
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作者 Yue Wang Fuzheng Gao 《Journal of Computational Mathematics》 SCIE CSCD 2025年第4期898-917,共20页
A weak Galerkin mixed finite element method is studied for linear elasticity problems without the requirement of symmetry.The key of numerical methods in mixed formulation is the symmetric constraint of numerical stre... A weak Galerkin mixed finite element method is studied for linear elasticity problems without the requirement of symmetry.The key of numerical methods in mixed formulation is the symmetric constraint of numerical stress.In this paper,we introduce the discrete symmetric weak divergence to ensure the symmetry of numerical stress.The corresponding stabilizer is presented to guarantee the weak continuity.This method does not need extra unknowns.The optimal error estimates in discrete H1 and L2 norms are established.The numerical examples in 2D and 3D are presented to demonstrate the efficiency and locking-free property. 展开更多
关键词 Linear elasticity Discrete symmetric weak divergence Mixed finite element method Weak Galerkin finite element method
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SUPERCONVERGENCE ERROR ESTIMATES OF THE LOWEST-ORDER RAVIART-THOMAS GALERKIN MIXED FINITE ELEMENT METHOD FOR NONLINEAR THERMISTOR EQUATIONS 认领 引用
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作者 Huaijun Yang Dongyang Shi 《Journal of Computational Mathematics》 SCIE CSCD 2025年第6期1548-1574,共27页
This paper is concerned with the superconvergence error estimates of a classical mixed finite element method for a nonlinear parabolic/elliptic coupled thermistor equations.The method is based on a popular combination... This paper is concerned with the superconvergence error estimates of a classical mixed finite element method for a nonlinear parabolic/elliptic coupled thermistor equations.The method is based on a popular combination of the lowest-order rectangular Raviart-Thomas mixed approximation for the electric potential/field(φ,θ)and the bilinear Lagrange approximation for temperature u.In terms of the special properties of these elements above,the superclose error estimates with order O(h2)are obtained firstly for all three components in such a strongly coupled system.Subsequently,the global superconvergence error estimates with order O(h2)are derived through a simple and effective interpolation post-processing technique.As by a product,optimal error estimates are acquired for potential/field and temperature in the order of O(h)and O(h2),respectively.Finally,some numerical results are provided to confirm the theoretical analysis. 展开更多
关键词 Nonlinear thermistor equations Galerkin mixed finite element method Interpolation post-processing technique Superclose and superconvergence error estimates
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An Arbitrary Order Mixed Finite Element Method with Boundary Value Correction for the Darcy Flow on Curved Domains 认领 引用
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作者 Yongli Hou Yanqiu Wang 《Communications in Computational Physics》 SCIE CSCD 2025年第5期1227-1249,共23页
We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains.The discretization... We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains.The discretization is defined on a body-fitted triangular mesh,i.e.the boundary nodes of the mesh lie on the curved physical boundary.However,the boundary edges of the triangular mesh,which are straight,may not coincide with the curved physical boundary.A boundary value correction technique is then designed to transform the Neumann boundary condition from the physical boundary to the boundary of the triangular mesh.One advantage of the boundary value correction method is that it avoids using curved mesh elements and thus reduces the complexity of implementation.We prove that the proposed method reaches optimal convergence for arbitrary order discretizations.Supporting numerical results are presented. 展开更多
关键词 Mixed finite element method Neumann boundary condition curved domain boundary value correction method
A MIXED FINITE ELEMENT AND UPWIND MIXED FINITE ELEMENT MULTI-STEP METHOD FOR THE THREE-DIMENSIONAL POSITIVE SEMI-DEFINITE DARCY-FORCHHEIMER MISCIBLE DISPLACEMENT PROBLEM 认领 引用
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作者 Yirang YUAN Changfeng LI +1 位作者 Huailing SONG Tongjun SUN 《Acta Mathematica Scientia》 SCIE CSCD 2025年第2期715-736,共22页
In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e... In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application. 展开更多
关键词 Darcy-Forchheimer fow three-dimensional positive semi-definite problem upwind mixed finite element multi-step method conservation of mass convergence analysis
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A Mixed Finite Element Method for Vibration Problems of Non-Homogeneous Damped Beams 认领 引用
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作者 Yuqian Ye Wenhui Ma +1 位作者 Manyu Wang Ailing Zhu 《Engineering（科研）》 2025年第3期189-206,共18页
Beam is one of the common structures in engineering,with the development of technology,homogeneous beams no longer meet the needs of engineering structural design,for this reason,people have researched the non-homogen... Beam is one of the common structures in engineering,with the development of technology,homogeneous beams no longer meet the needs of engineering structural design,for this reason,people have researched the non-homogeneous beams.In this paper,we study the mixed finite element method for the vibration problem of non-homogeneous damped beams.The fourth-order differential equations are transformed into a system of low-order partial differential equations by introducing intermediate variables,constructing a semidiscrete extended mixed finite element format,proving the existence and uniqueness of the solution of the format,and utilizing the elliptic projection operator for the error estimation.The time derivative term is discretized by the central difference,and the fully discrete mixed element format is given to prove the stability and convergence of the format.The feasibility and effectiveness of the mixed method are verified by numerical examples,and the effects of different damping coefficientsμon beam vibration are investigated. 展开更多
关键词 Non-Homogeneous Damped Beams Mixed Finite Element Methods Error Estimation
Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods 认领 引用 被引量：5
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作者 Yanping Chen Peng Luan Zuliang Lu 《Advances in Applied Mathematics and Mechanics》 SCIE 2009年第6期830-844,共15页
In this paper,we present an efficient method of two-grid scheme for the approximation of two-dimensional nonlinear parabolic equations using an expanded mixed finite element method.We use two Newton iterations on the ... In this paper,we present an efficient method of two-grid scheme for the approximation of two-dimensional nonlinear parabolic equations using an expanded mixed finite element method.We use two Newton iterations on the fine grid in our methods.Firstly,we solve an original nonlinear problem on the coarse nonlinear grid,then we use Newton iterations on the fine grid twice.The two-grid idea is from Xu's work[SIAM J.Numer.Anal.,33(1996),pp.1759–1777]on standard finite method.We also obtain the error estimates for the algorithms of the two-grid method.It is shown that the algorithm achieve asymptotically optimal approximation rate with the two-grid methods as long as the mesh sizes satisfy h=O(H(4k+1/(k+1))). 展开更多
关键词 Nonlinear parabolic equations two-grid scheme expanded mixed finite element methods Gronwall’s Lemma
Superconvergence Analysis of Splitting Positive Definite Nonconforming Mixed Finite Element Method for Pseudo-hyperbolic Equations 认领 引用 被引量：7
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作者 Dong-yang SHI Qi-li TANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第4期843-854,共12页
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bil... In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes. 展开更多
关键词 pseudo-hyperbolic equations splitting positive definite nonconforming mixed finite element method,superclose superconvergence
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Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem 认领 引用 被引量：3
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作者 Yanping Chen Li Dai Zuliang Lu 《Advances in Applied Mathematics and Mechanics》 SCIE 2010年第1期56-75,共20页
We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods.We use the lowest order Raviart-Thomas mix... We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods.We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control variable.We obtain the superconvergence of O(h1+s)(0<s≤1)for the control variable.Finally,we present two numerical examples to confirm our superconvergence results. 展开更多
关键词 Constrained optimal control problem linear elliptic equation mixed finite element methods rectangular partition superconvergence properties
A posteriori error estimator for eigenvalue problems by mixed finite element method 认领 引用 被引量：2
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作者 JIA ShangHui CHEN HongTao XIE HeHu 《Science China Mathematics》 SCIE EI 2013年第5期887-900,共14页
In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergenc... In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments. 展开更多
关键词 second order elliptic eigenvalue problem mixed finite element method Raviart-Thomas a pos- teriori error estimate adaptive
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