Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H(div;Ω)×H1(Ω) norms error estima...Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H(div;Ω)×H1(Ω) norms error estimates standard mixed finite spaces. Moreover, these two schemes provide the with first-order and second-order accuracy in time increment, respectively.展开更多
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
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi...A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.展开更多
In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the line...In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.展开更多
Discretising a structure into elements is a key step in finite element(FE)analysis.The discretised geometry used to formulate an FE model can greatly affect accuracy and validity.This paper presents a unified dimensio...Discretising a structure into elements is a key step in finite element(FE)analysis.The discretised geometry used to formulate an FE model can greatly affect accuracy and validity.This paper presents a unified dimensionless parameter to generate a mesh of cubic FEs for the analysis of very long beams resting on an elastic foundation.A uniform beam resting on elastic foundation with various values of flexural stiffness and elastic supporting coefficients subject to static load and moving load is used to illustrate the application of the proposed parameter.The numerical results show that(a)Even if the values of the flexural stiffness of the beam and elastic supporting coefficient of the elastic foundation are different,the same proposed parameter“s”can ensure the same accuracy of the FE solution,but the accuracy may differ for use of the same element length;(b)The proposed dimensionless parameter“s”can indeed be used as a unified index to generate the mesh for a beam resting on elastic foundation,whereas the use of the same element length as a criterion may be misleading;(c)The errors between the FE and analytical solutions for the maximum vertical displacement,shear force and bending moment of the beam increase with the dimensionless parameter“s”;and(d)For the given allowable errors for the vertical displacement,shear force and bending moment of the beam under static load and moving load,the corresponding values of the proposed parameter are provided to guide the mesh generation.展开更多
An internal failure mode for a soil-nailed system consists of failure at nail heads,slope facing,nail strength,along groutesoil interface and pullout failure.A better understanding of pullout of soil nail thus becomes...An internal failure mode for a soil-nailed system consists of failure at nail heads,slope facing,nail strength,along groutesoil interface and pullout failure.A better understanding of pullout of soil nail thus becomes important to assess the stability of a soil-nailed system.In the present study,an investigation into the pullout behaviour of soil nail with circular discs along the shaft has been carried out by a threedimensional finite element analysis using Abaqus/Explicit routine.A total of 67 simulations have been performed to accurately predict the pullout behaviour of soil nail.The soil nail under study has circular discs along its shaft varying in numbers from 1 to 4.The pullout of this soil nail in a pullout test box has been simulated with a constant overburden pressure of 20 kPa acting on the nail.The pullout load edisplacement characteristics,stresses around soil nail and failure mechanism during pullout are studied.Variations of dimensionless factors such as normalised pullout load factor and bearing capacity factor have been obtained with different combinations of parameters in terms of relative disc spacing ratio,anchorage length ratio,embedment ratio,diameter ratio and displacement ratio.From the results of analyses,it is found that nail with more circular discs requires higher pullout load.There are critical relative disc spacing ratio and diameter ratio which significantly affect the pullout behaviour of nail.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, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite...In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived. [ABSTRACT FROM AUTHOR]展开更多
In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element sp...In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection, superconvergent H1-error estimates of both the primary solution approximation uh and the flux approximation σh are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(hr+2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-Douglas-Fortin-Marini elements of order r are employed with optimal error estimate of O(hr+1).展开更多
In this paper, a constrained distributed optimal control problem governed by a first- order elliptic system is considered. Least-squares mixed finite element methods, which are not subject to the Ladyzhenkaya-Babuska-...In this paper, a constrained distributed optimal control problem governed by a first- order elliptic system is considered. Least-squares mixed finite element methods, which are not subject to the Ladyzhenkaya-Babuska-Brezzi consistency condition, are used for solving the elliptic system with two unknown state variables. By adopting the Lagrange multiplier approach, continuous and discrete optimality systems including a primal state equation, an adjoint state equation, and a variational inequality for the optimal control are derived, respectively. Both the discrete state equation and discrete adjoint state equation yield a symmetric and positive definite linear algebraic system. Thus, the popular solvers such as preconditioned conjugate gradient (PCG) and algebraic multi-grid (AMG) can be used for rapid solution. Optimal a priori error estimates are obtained, respectively, for the control function in L2 (Ω)-norm, for the original state and adjoint state in H1 (Ω)-norm, and for the flux state and adjoint flux state in H(div; Ω)-norm. Finally, we use one numerical example to validate the theoretical findings.展开更多
Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio...Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Information on the least-squares mixed element schemes for nonlinear parabolic problem.展开更多
基金Supported by by the National Science Foundation for Young Scholars of China(11101431)the Fundamental Research Funds for the Central Universities (12CX04082A,10CX04041A)Shandong Province Natural Science Foundation of China(ZR2010AL020)
文摘Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H(div;Ω)×H1(Ω) norms error estimates standard mixed finite spaces. Moreover, these two schemes provide the with first-order and second-order accuracy in time increment, respectively.
文摘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.
文摘A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.
文摘In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.
基金the National Key Research and Development Program of China(Grant 2017YFB1201204)National Natural Science Foundation of China(Grants 51578552,U1334203).
文摘Discretising a structure into elements is a key step in finite element(FE)analysis.The discretised geometry used to formulate an FE model can greatly affect accuracy and validity.This paper presents a unified dimensionless parameter to generate a mesh of cubic FEs for the analysis of very long beams resting on an elastic foundation.A uniform beam resting on elastic foundation with various values of flexural stiffness and elastic supporting coefficients subject to static load and moving load is used to illustrate the application of the proposed parameter.The numerical results show that(a)Even if the values of the flexural stiffness of the beam and elastic supporting coefficient of the elastic foundation are different,the same proposed parameter“s”can ensure the same accuracy of the FE solution,but the accuracy may differ for use of the same element length;(b)The proposed dimensionless parameter“s”can indeed be used as a unified index to generate the mesh for a beam resting on elastic foundation,whereas the use of the same element length as a criterion may be misleading;(c)The errors between the FE and analytical solutions for the maximum vertical displacement,shear force and bending moment of the beam increase with the dimensionless parameter“s”;and(d)For the given allowable errors for the vertical displacement,shear force and bending moment of the beam under static load and moving load,the corresponding values of the proposed parameter are provided to guide the mesh generation.
文摘An internal failure mode for a soil-nailed system consists of failure at nail heads,slope facing,nail strength,along groutesoil interface and pullout failure.A better understanding of pullout of soil nail thus becomes important to assess the stability of a soil-nailed system.In the present study,an investigation into the pullout behaviour of soil nail with circular discs along the shaft has been carried out by a threedimensional finite element analysis using Abaqus/Explicit routine.A total of 67 simulations have been performed to accurately predict the pullout behaviour of soil nail.The soil nail under study has circular discs along its shaft varying in numbers from 1 to 4.The pullout of this soil nail in a pullout test box has been simulated with a constant overburden pressure of 20 kPa acting on the nail.The pullout load edisplacement characteristics,stresses around soil nail and failure mechanism during pullout are studied.Variations of dimensionless factors such as normalised pullout load factor and bearing capacity factor have been obtained with different combinations of parameters in terms of relative disc spacing ratio,anchorage length ratio,embedment ratio,diameter ratio and displacement ratio.From the results of analyses,it is found that nail with more circular discs requires higher pullout load.There are critical relative disc spacing ratio and diameter ratio which significantly affect the pullout behaviour of nail.
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).
文摘In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived. [ABSTRACT FROM AUTHOR]
基金Supported by National Science Foundation of China and the Foundation of China State Education Commission and the Special Funds for Major State Basic Research Projects.
文摘In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection, superconvergent H1-error estimates of both the primary solution approximation uh and the flux approximation σh are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(hr+2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-Douglas-Fortin-Marini elements of order r are employed with optimal error estimate of O(hr+1).
基金Acknowledgements. The authors would like to thank the editor and the anonymous referee for their valuable comments and suggestions on an earlier version of this paper. The work of Hongxing Rui (corresponding author) was supported by the NationM Natural Science Founda- tion of China (No. 11171190). The work of Hongfei Fu was supported by the National Natural Science Foundation of China (No. 11201485), the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (No. BS2013NJ001), and the Fundamental Research Funds for the Central Universities (No. 14CX02217A).
文摘In this paper, a constrained distributed optimal control problem governed by a first- order elliptic system is considered. Least-squares mixed finite element methods, which are not subject to the Ladyzhenkaya-Babuska-Brezzi consistency condition, are used for solving the elliptic system with two unknown state variables. By adopting the Lagrange multiplier approach, continuous and discrete optimality systems including a primal state equation, an adjoint state equation, and a variational inequality for the optimal control are derived, respectively. Both the discrete state equation and discrete adjoint state equation yield a symmetric and positive definite linear algebraic system. Thus, the popular solvers such as preconditioned conjugate gradient (PCG) and algebraic multi-grid (AMG) can be used for rapid solution. Optimal a priori error estimates are obtained, respectively, for the control function in L2 (Ω)-norm, for the original state and adjoint state in H1 (Ω)-norm, and for the flux state and adjoint flux state in H(div; Ω)-norm. Finally, we use one numerical example to validate the theoretical findings.
基金Major State Basic Research Program of People's Republic of China(G1999032803).
文摘Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Information on the least-squares mixed element schemes for nonlinear parabolic problem.