线性对流占优扩散方程的扩展特征混合有限元法

本文针对线性对流占优扩散方程提出了一种新型数值模拟方法一扩展特征混合有限元法,即对对流部分沿特征线方向离散,而对扩散部分采用扩展混合有限元方法,同时高精度逼近未知函数,未知函数的梯度及伴随向量函数,通过严格的数值分析,得到其最优L^2模误差估计。     

对流占优问题稳定化的扩展混合有限元方法

讨论了对流占优问题稳定化的扩展混合元数值模拟.把稳定化的思想与扩展混合元方法相结合,既可以高精度逼近未知函数,未知函数的梯度及伴随向量函数,又能保证格式的稳定性.理论分析表明,方法是有效的,具有最优L²逼近精度.     

对流占优扩散方程的分裂特征混合有限元方法

利用修正的特征线方法,构建一类求解对流占优扩散方程的分裂特征混合有限元算法.在新的算法中,混合系统的系数矩阵对称正定,且原未知函数u与流函数σ=-ε▽u可分离求解.推导了加权能量模意义下的最优阶误差估计,并给出数值算例验证理论上的分析结果.     

线性对流占优Sobolev方程的流线扩散有限元方法

Abastract. In this paper,a streamline-diffusion F. E. M. for linear Sobolev equations with con-vection-dominated term is given. According to the range of space-time F. E mesh parameter h,two choices for artifical diffusion parameter are presented,and for the corresponding computa-tion schemes the stability and error estimates in suitable norms are estabilished.     

对流占优扩散方程的特征有限体积元方法

考虑对流占优扩散方程初边值问题的特征有限体积元方法,并给出特征有限体积元解的误差分析.理论分析表明特征有限体积元解具有最优阶L~2和H~1模误差估计.数值算例说明此方法是有效的.     

一种非线性对流扩散方程的特征有限元方法的误差估计

给出求解一种二维非线性对流扩散方程组的Grank-Nicolson型特征有限元方法，并给出该方法的H^1模最优误差估计。     

一种非线性对流扩散方程的特征有限元方法的误差估计

给出求解一种二维非线性对流扩散方程组的 Grank-Nicolson型特征有限元方法 ,并给出该方法的 H1模最优阶误差估计 .     

线性对流占优扩散方程的后验误差估计

对于线性对流占优扩散方程,采用特征线有限元方法离散时间导数项和对流项,用分片线性有限元离散空间扩散项,并给出了一致的后验误差估计,其中估计常数不依赖与扩散项系数。     

椭圆型对流占优扩散方程的泡函数—混合有限元方法(英文)

把泡函数有限元方法和混合有限元方法进行耦合,从而利用泡函数-混合有限元方法来求解椭圆型对流占优扩散方程,该方法不仅可以同时高精度逼近浓度(u)和浓度变化率(#u),还有效避开了传统混合有元方法中苛刻的L-BB条件,数值解的稳定性也得到了改善.     

对流扩散方程的有限体积-有限元方法的误差估计

本文结合有限体积方法和有限元方法处理非线性对流扩散问题,非线性对流项利用有限体积方法处理,扩散项利用有限元方法离散,并给近似解的误差估计。     

对流扩散问题流线扩散法的最优误差估计

在本文中,我们考虑对流占优扩散问题流线扩散双线性有限元方法。原先的文献在ε≤h~2的条件下,得到了L~2-模最优误差估计,而本文则在ε≤h的条件下得到了相同估计。     

一维定常型对流占优扩散方程的一类迎风有限体积格式

本文针对一维定常型对流占优扩散方程提出了一类迎风有限体积格式 .该格式对对流项具有二阶精度 ,对扩散项保持一阶精度 ,符合对流占优扩散问题强对流、弱扩散的特点 .     

A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS I： SPATIAL DISCRETIZATION

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.     

Some A Posteriori Error Estimates of the Finite-Difference Streamline-Diffusion Method for Convection-Dominated Diffusion Equations

In this paper, some a posteriori error estimates of the finite-difference streamline-diffusion method for one- and two-dimensional time-dependent convection-dominated diffusion equations are presented, which can be used to reasonably adjust space mesh. Numerical results show that this method of local refinement is feasible and effective.     

一类非定常对流占优扩散问题差分-流线扩散法的后处理

讨论了一类非定常对流占优扩散方程的差分-流线扩散格式(FDSD),利用插值后处理技术,提高了特殊网格下该FDSD格式在双线性元空间的精度,从而按L∞(L2(Ω) 模达到最优．     

Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations

In this paper, we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients. There are two contributions of this paper. Firstly, we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space, which is competitive for high-dimensional random inputs. Secondly, the a priori error estimates are derived for the state,the co-state and the control variables. Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.     

Discontinuous Hybrid Primal Finite Element Method for Elliptic Equations

A primal hybrid finite element scheme is introduced to produce completely discontinuous solution for diffusion and convection-diffusion problems. Same rate of convergence as classical methods is obtained in suitable norms. Finally an a posteriori error estimator is given.     

非线性波动方程的各向异性有限元方法

研究了非线性波动方程的各向异性有限元方法,得到了半离散格式下的最优误差估计.     

A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations

Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + h k+1 + H 2k+2 d/2 ) (k ≥ 1), where k is the degree of the approximating ...