The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have diff...The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.展开更多
The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent ...The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.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
Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a ...Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.展开更多
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
In this paper, the random interval equilibrium equations (RIEE) is obtained by lambda-level cutting the fuzzy-stochastic finite element equilibrium equations (FSFEEE). Based on the relations between the variables of e...In this paper, the random interval equilibrium equations (RIEE) is obtained by lambda-level cutting the fuzzy-stochastic finite element equilibrium equations (FSFEEE). Based on the relations between the variables of equilibrium equations, solving RIEE is transformed into solving two kinds of general random equilibrium equations (GREE). Then the recursive equations of evaluating the random interval displacement is derived from the small-parameter perturbation theory. The computational formulae of statistical characteristic of the fuzzy random displacements, the fuzzy random strains and the fuzzy random stresses are also deduced in detail.展开更多
A speedy accurate solution to structural fuzzy finite element equilibrium equations (SFFEEE), by combining the definition of the solution of interval equations with the mechanical meaning of the structural finite elem...A speedy accurate solution to structural fuzzy finite element equilibrium equations (SFFEEE), by combining the definition of the solution of interval equations with the mechanical meaning of the structural finite element equilibrium equations (SFEEE), was put forward. The fuzzification of the SFFEEE, which is discussed in this paper, originates from that of material property, structural boundary conditions and external loading. The computing quantity of this solution is almost equal to that of the general finite element method (GFEM).展开更多
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
A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is d...A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.展开更多
A highly efficient H1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation ...A highly efficient H1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h^2) for both the original variable u in H1 (Ω) norm and the flux p = u in H(div, Ω) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h^3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.展开更多
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me...In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.展开更多
The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space ...The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).展开更多
Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine fini...Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.展开更多
In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error est...In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton (or semi-Newton) iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover, the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.展开更多
In this paper,Runge-Kutta Discontinuous Galerkin(RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin(RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ?ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ?ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conf...The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conforming or consistent in the sense that no projection/reduction is introduced.Theoretical proof and numerical confirmation are presented.展开更多
A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements f...A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.展开更多
This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element a...This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.展开更多
In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computat...In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.展开更多
文摘The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.
文摘The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.
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.
文摘Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.
文摘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.
文摘In this paper, the random interval equilibrium equations (RIEE) is obtained by lambda-level cutting the fuzzy-stochastic finite element equilibrium equations (FSFEEE). Based on the relations between the variables of equilibrium equations, solving RIEE is transformed into solving two kinds of general random equilibrium equations (GREE). Then the recursive equations of evaluating the random interval displacement is derived from the small-parameter perturbation theory. The computational formulae of statistical characteristic of the fuzzy random displacements, the fuzzy random strains and the fuzzy random stresses are also deduced in detail.
文摘A speedy accurate solution to structural fuzzy finite element equilibrium equations (SFFEEE), by combining the definition of the solution of interval equations with the mechanical meaning of the structural finite element equilibrium equations (SFEEE), was put forward. The fuzzification of the SFFEEE, which is discussed in this paper, originates from that of material property, structural boundary conditions and external loading. The computing quantity of this solution is almost equal to that of the general finite element method (GFEM).
基金Supported by the National Natural Science Foundation of China (10601022)Natural Science Foundation of Inner Mongolia Autonomous Region (200607010106)Youth Science Foundation of Inner Mongolia University(ND0702)
文摘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.
基金Supported by the National Natural Science Foundation of China (10671184)
文摘A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.
基金Project supported by the National Natural Science Foundation of China(Nos.10971203,11271340,and 11101381)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘A highly efficient H1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h^2) for both the original variable u in H1 (Ω) norm and the flux p = u in H(div, Ω) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h^3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
基金heprojectissupportedbyNNSFofChina (No .1 9972 0 39) .
文摘In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.
文摘The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).
基金Project supported by the National Natural Science Foundation of China (No. 10371096)
文摘Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.
基金supported by the National Natural Science Foundation of China(Nos.11461068,11362021,and 11401511)the Doctoral Foundation of Xinjiang Uygur Autonomous Region of China(No.BS110101)
文摘In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton (or semi-Newton) iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover, the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin(RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ?ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ?ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
文摘The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conforming or consistent in the sense that no projection/reduction is introduced.Theoretical proof and numerical confirmation are presented.
基金supported by the National Natural Science Foundation of China(Nos.11271273 and 11271298)
文摘A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.
基金Project supported by the National Natural Science Foundation of China(No.11271340)
文摘This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.
基金the National Natural Science Foundation of China and China State Key Project for Basic Researches
文摘In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.