The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the stren...The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the strengths of the reinforcement members and soils are reduced with the same factor. While using the SRM, only soil strength is reduced during the calculation of the factor of safety. This causes inconsistence in calculating the factor of safety of the MSE structures. To overcome this, an iteration method is proposed to consider the strength reduction of the reinforcements in SRM. The method is demonstrated by using PLAXIS, a finite element software. The results show that the factor of safety converges after a few iterations. The reduction of strength has different effects on the factor of safety depending on the properties of the reinforcements and the soil, and failure modes.展开更多
Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this pap...Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.展开更多
We take the two dimensional vorticity equations as models to describe spectral methods and their combinations with finite difference methods or finite element methods, which are applicable to other similar nonlinear ...We take the two dimensional vorticity equations as models to describe spectral methods and their combinations with finite difference methods or finite element methods, which are applicable to other similar nonlinear problems. Some numerical results and error estimates of these methods are given.展开更多
A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis i...A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.展开更多
In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-...In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases.Firstly,the spectral property of the DG method is analyzed using the approximate dispersion relation(ADR)method and compared with typical finite difference methods,which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error.Then several typical test cases relevant to problems of compressible turbulence are simulated,including one-dimensional shock/entropy wave interaction,two-dimensional decaying isotropic turbulence,and two-dimensional temporal mixing layers.Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes.Furthermore,shocks are also well captured using the localized artificial diffusivity method.The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.展开更多
A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L^2(‖·‖_h)norm isobtained through Ritz...A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L^2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.展开更多
This paper extends the unifying theory for a posteriori error analysis of the nonconformingfinite element methods to the second order elliptic eigenvalue problem.In particular,the authorproposes the a posteriori error...This paper extends the unifying theory for a posteriori error analysis of the nonconformingfinite element methods to the second order elliptic eigenvalue problem.In particular,the authorproposes the a posteriori error estimator for nonconforming methods of the eigenvalue problems andprove its reliability and efficiency based on two assumptions concerning both the weak continuity andthe weak orthogonality of the nonconforming finite element spaces,respectively.In addition,the authorexamines these two assumptions for those nonconforming methods checked in literature for the Laplace,Stokes,and the linear elasticity problems.展开更多
基金Project(41072200)supported by the National Natural Science Foundation of ChinaProject(14PJD032)supported by the Shanghai Pujiang Program,China
文摘The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the strengths of the reinforcement members and soils are reduced with the same factor. While using the SRM, only soil strength is reduced during the calculation of the factor of safety. This causes inconsistence in calculating the factor of safety of the MSE structures. To overcome this, an iteration method is proposed to consider the strength reduction of the reinforcements in SRM. The method is demonstrated by using PLAXIS, a finite element software. The results show that the factor of safety converges after a few iterations. The reduction of strength has different effects on the factor of safety depending on the properties of the reinforcements and the soil, and failure modes.
文摘Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.
文摘We take the two dimensional vorticity equations as models to describe spectral methods and their combinations with finite difference methods or finite element methods, which are applicable to other similar nonlinear problems. Some numerical results and error estimates of these methods are given.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10671184 and 10971203.
文摘A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.
基金supported by the National Basic Research Program of China(Grant No.2009CB724104)
文摘In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases.Firstly,the spectral property of the DG method is analyzed using the approximate dispersion relation(ADR)method and compared with typical finite difference methods,which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error.Then several typical test cases relevant to problems of compressible turbulence are simulated,including one-dimensional shock/entropy wave interaction,two-dimensional decaying isotropic turbulence,and two-dimensional temporal mixing layers.Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes.Furthermore,shocks are also well captured using the localized artificial diffusivity method.The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.
基金supported by the Natural Science Foundation of China under Grant Nos.10671184 and 10971203
文摘A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L^2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.
文摘This paper extends the unifying theory for a posteriori error analysis of the nonconformingfinite element methods to the second order elliptic eigenvalue problem.In particular,the authorproposes the a posteriori error estimator for nonconforming methods of the eigenvalue problems andprove its reliability and efficiency based on two assumptions concerning both the weak continuity andthe weak orthogonality of the nonconforming finite element spaces,respectively.In addition,the authorexamines these two assumptions for those nonconforming methods checked in literature for the Laplace,Stokes,and the linear elasticity problems.
