In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-valu...In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavelet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.展开更多
The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and ...The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and superconvergence results are proved without any time-step restriction condition for the proposed scheme.The proof consists of three ingredients.First,a temporal-spatial error splitting argument is employed to bound the numerical solution in certain strong norms.Second,optimal error estimates are derived through a novel splitting technique to deal with the time derivative and some sharp estimates to cope with the nonlinear terms.Third,by virtue of the relationship between the Ritz projection and the interpolation,as well as a so-called"lifting"technique,the superconvergence behavior of order O(h^(2)+τ^(2))in H^(1)-norm for the original variables are deduced.Finally,a numerical experiment is conducted to confirm our theoretical analysis.Here,h is the spatial subdivision parameter,andτis the time step.展开更多
The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 err...The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.展开更多
In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element schem...In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element scheme is used for the discretization in the spatial direction,and the temporal component is discretized by a new alternating direction implicit(ADI)method.Next,we strictly prove that the numerical method is stable and convergent.Finally,to confirm our theoretical analysis,some numerical examples in 2D space are presented.展开更多
对于结构动力分析中的离散系统运动方程,现有算法的计算精度和效率均依赖于时间步长的选取,这是时间域问题求解的难点.基于EEP(element energy projection)超收敛计算的自适应有限元法,以EEP超收敛解代替未知真解,估计常规有限元解的误...对于结构动力分析中的离散系统运动方程,现有算法的计算精度和效率均依赖于时间步长的选取,这是时间域问题求解的难点.基于EEP(element energy projection)超收敛计算的自适应有限元法,以EEP超收敛解代替未知真解,估计常规有限元解的误差,并自动细分网格,目前已对诸类以空间坐标为自变量的边值问题取得成功.对离散系统运动方程建立弱型Galerkin有限元解,引入基于EEP法的自适应求解策略,在时间域上自动划分网格,最终得到所求时域内任一时刻均满足给定误差限的动位移解,进而建立了一种时间域上的新型自适应求解算法.展开更多
A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct fea...A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured,whereas the discontinuity of the velocity vector at the discrete time levels still remains.The computational cost is then obviously reduced, particularly,for material non-linear problems.Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed.Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.展开更多
A Computational Fluid Dynamic (CFD) model is presented to analyze the flow dynamics of a two phase incompressible flow in the application sectors of different industries. The Finite Element method (FEM) which is based...A Computational Fluid Dynamic (CFD) model is presented to analyze the flow dynamics of a two phase incompressible flow in the application sectors of different industries. The Finite Element method (FEM) which is based on the Galerkin approximation, has been implemented for this two phase flow model. Generally, two-phase flows can occur in different forms like gas-liquid, liquid-liquid and solid-liquid forms. The Oil and Water two-phase flow is an important phenomenon in petroleum industry for crude oil production and transportation. In our study, a laminar flow of liquid-liquid phase is considered to simulate the flow dynamics where the liquid phases are water and oil. The COMSOL Multiphysics software is used to perform the simulation including velocity profile, volume fraction, shear rate, pressure distributions and interfacial thicknesses at different times. A typical circular tube domain with radius 0.05 m and length 8 m is assumed for our simulation.展开更多
文摘In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavelet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.
基金supported by the National Natural Science Foundation of China(No.11671369,No.12071443)Key Scientific Research Project of Colleges and Universities in Henan Province(No.20B110013).
文摘The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and superconvergence results are proved without any time-step restriction condition for the proposed scheme.The proof consists of three ingredients.First,a temporal-spatial error splitting argument is employed to bound the numerical solution in certain strong norms.Second,optimal error estimates are derived through a novel splitting technique to deal with the time derivative and some sharp estimates to cope with the nonlinear terms.Third,by virtue of the relationship between the Ritz projection and the interpolation,as well as a so-called"lifting"technique,the superconvergence behavior of order O(h^(2)+τ^(2))in H^(1)-norm for the original variables are deduced.Finally,a numerical experiment is conducted to confirm our theoretical analysis.Here,h is the spatial subdivision parameter,andτis the time step.
基金supported in part by a grant from National Science Foundation(Project No.11301262)a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613)The work of J.Wang and W.Sun was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613).
文摘The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.
基金NSF of China[grant number:11371157]Natural Science Foundation of Anhui Higher Education Institutions of China[grant number:KJ2016A492]Natural Science Foundation of Bozhou College[grant number:BSKY201426,BSKY201535].
文摘In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element scheme is used for the discretization in the spatial direction,and the temporal component is discretized by a new alternating direction implicit(ADI)method.Next,we strictly prove that the numerical method is stable and convergent.Finally,to confirm our theoretical analysis,some numerical examples in 2D space are presented.
文摘对于结构动力分析中的离散系统运动方程,现有算法的计算精度和效率均依赖于时间步长的选取,这是时间域问题求解的难点.基于EEP(element energy projection)超收敛计算的自适应有限元法,以EEP超收敛解代替未知真解,估计常规有限元解的误差,并自动细分网格,目前已对诸类以空间坐标为自变量的边值问题取得成功.对离散系统运动方程建立弱型Galerkin有限元解,引入基于EEP法的自适应求解策略,在时间域上自动划分网格,最终得到所求时域内任一时刻均满足给定误差限的动位移解,进而建立了一种时间域上的新型自适应求解算法.
基金The project supported by the National Natural Science Foundation of China(19832010,50278012,10272027)the National Key Basic Research and Development Program(973 Program,2002CB412709)
文摘A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured,whereas the discontinuity of the velocity vector at the discrete time levels still remains.The computational cost is then obviously reduced, particularly,for material non-linear problems.Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed.Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.
文摘A Computational Fluid Dynamic (CFD) model is presented to analyze the flow dynamics of a two phase incompressible flow in the application sectors of different industries. The Finite Element method (FEM) which is based on the Galerkin approximation, has been implemented for this two phase flow model. Generally, two-phase flows can occur in different forms like gas-liquid, liquid-liquid and solid-liquid forms. The Oil and Water two-phase flow is an important phenomenon in petroleum industry for crude oil production and transportation. In our study, a laminar flow of liquid-liquid phase is considered to simulate the flow dynamics where the liquid phases are water and oil. The COMSOL Multiphysics software is used to perform the simulation including velocity profile, volume fraction, shear rate, pressure distributions and interfacial thicknesses at different times. A typical circular tube domain with radius 0.05 m and length 8 m is assumed for our simulation.
