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
On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these meth...On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.展开更多
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
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlin...A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.展开更多
Mixed element formats of any order based on bubble functions for the stationary Stokes problem are derived in triangular and tetrahedral meshes and the convergence of these formats are proved.
Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacita...Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacitance increases quasi-quadratically with the number of electrodes increasing.The quasi-quadratic dependence can be explained by a sequence of lumped capacitors connected in parallel.For a photomixer composed of 10 electrodes and 9 photoconductive gaps,the finger capacitance increases as the gap width increases at a small electrode width,and follows the reverse trend at a large electrode width.For a constant electrode width,the finger capacitance first decreases and then slightly increases as the gap broadens until the smallest finger capacitance is formed.We also investigate the finger capacitances at different electrode and gap configurations with the 8 μm × 8 μm photomixer commonly used in previous studies.These calculations lead to a better understanding of the finger capacitance affected by the finger parameters,and should lead to terahertz photomixer optimization.展开更多
The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES...The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.展开更多
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.展开更多
H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and unique...H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.展开更多
Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the bu...Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equatio...In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.展开更多
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘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.
基金supported by NSFC(11571266,91430106,11171168,11071132)NSFC-RGC(China-Hong Kong)(11661161017)
文摘On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.
文摘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.
文摘A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
基金Supported by National Natural Science Foundation of China(11371331)Supported by the Natural Science Foundation of Education Department of Henan Province(14B110018)
文摘Mixed element formats of any order based on bubble functions for the stationary Stokes problem are derived in triangular and tetrahedral meshes and the convergence of these formats are proved.
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2011AAxxx2008A)Hundred Talent Program of the Chinese Academy of Sciences (Grant No. J08-029)the Main Direction Program of Knowledge Innovation of the Chinese Academy of Sciences (Grant No. YYYJ-1123-4)
文摘Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacitance increases quasi-quadratically with the number of electrodes increasing.The quasi-quadratic dependence can be explained by a sequence of lumped capacitors connected in parallel.For a photomixer composed of 10 electrodes and 9 photoconductive gaps,the finger capacitance increases as the gap width increases at a small electrode width,and follows the reverse trend at a large electrode width.For a constant electrode width,the finger capacitance first decreases and then slightly increases as the gap broadens until the smallest finger capacitance is formed.We also investigate the finger capacitances at different electrode and gap configurations with the 8 μm × 8 μm photomixer commonly used in previous studies.These calculations lead to a better understanding of the finger capacitance affected by the finger parameters,and should lead to terahertz photomixer optimization.
基金funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 107.02-2019.330。
文摘The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
基金Supported by NNSF(10601022,11061021)Supported by NSF of Inner Mongolia Au-tonomous Region(200607010106)Supported by SRP of Higher Schools of Inner Mongolia(NJ10006)
文摘H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.
文摘Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
基金supported by the National Science Foundation of China(11271127 and 11061009)Science Research Program of Guizhou(GJ[2011]2367)the Co-Construction Project of Beijing Municipal Commission of Education
文摘In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.
