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| 1 | ROBUST GLOBALLY DIVERGENCE-FREE WEAK GALERKIN METHODS FOR STOKES EQUATIONS显示文摘这份报纸建议并且分析柔韧的全球性没有分叉的弱 Galerkin (WG ) 的一个班有限元素方法为司烧方程。新方法使用 Pk/Pk-1 (k 1 ) 为在元素的内部的速度和压力的不连续的有限元素联合,和 piecewise Pl/Pk (l = k - 1, k ) 为内部元素的边界上的速度和压力的踪迹近似。我们的方法不仅产出全球性没有分叉的速度答案,而且关于雷纳兹数字有一致错误估计。数字实验被提供显示出建议方法的坚韧性。[从作者抽象] | Gang Chen Minfu Feng Xiaoping Xie | 2016 | Journal of Computational Mathematics2016，34，5： | 11 |
| 2 | A NEW STABILIZED SUBGRID EDDY VISCOSITY METHOD BASED ON PRESSURE PROJECTION AND EXTRAPOLATED TRAPEZOIDAL RULE FOR THE TRANSIENT NAVIER-STOKES EQUATIONS显示文摘我们由使用有限元素的最低的相等顺序的对基于为短暂海军司烧方程的压力设计和外推的 trapezoidal 统治考虑一个新 subgrid 旋涡粘性方法。计划稳定传送对流统治问题并且改善限制 inf 啜相容性稳定性。它包括为稳定的术语和计算为更高的顺序衍生物要求了的压力免费的参数有一些吸引人的特征。而且,它要求仅仅每时间从一个 Oseen 问题产生的线性系统的解决方案走并且有第二份订单时间的精确性。方法关于答案整齐完成最佳的精确性。[从作者抽象] | Minfu Feng Yanhong Bai Yinnian He Yanmei Qin | 2011 | Journal of Computational Mathematics2011，29，4： | 8 |
| 3 | A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING TRANSIENT NAVIER-STOKES EQUATIONS WITH HIGH REYNOLDS NUMBER显示文摘In this paper,we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure.We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme.The scheme is proven to possess the absolute stability and the optimal error estimates.Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods,Pet ro-Galerkin finite element method and st reamline diffusion method. | Chunmei Xie Minfu Feng | 2020 | Journal of Computational Mathematics2020，38，3： | 0 |
| 4 | A New L^(2)Projection Method for the Oseen Equations显示文摘In this paper,a new type of stabilized finite element method is discussed for Oseen equations based on the local L^(2)projection stabilized technique for the velocity field.Velocity and pressure are approximated by two kinds of mixed finite element spaces,P^(2)_( l)-P_(1),(l=1,2).A main advantage of the proposed method lies in that,all the computations are performed at the same element level,without the need of nested meshes or the projection of the gradient of velocity onto a coarse level.Stability and convergence are proved for two kinds of stabilized schemes.Numerical experiments confirm the theoretical results. | Yanhong Bai Minfu Feng | 2017 | Advances in Applied Mathematics and Mechanics2017，9，6： | 0 |
| 5 | A FULL DISCRETE STABILIZED METHOD FOR THE OPTIMAL CONTROL OF THE UNSTEADY NAVIER-STOKES EQUATIONS显示文摘在这份报纸,完整的分离本地设计稳定了(LPS ) 方法被建议与相等的顺序元素解决不稳定的海军司烧方程的最佳的控制问题。对流效果和压力被使用 LPS 方法两个都稳定。一个 priori 错误关于雷纳兹一致地估计数字被获得,提供真答案是足够的光滑。数字实验被实现说明并且证实我们的理论分析。 | Yanmei Qin Gang Chen Minfu Feng | 2018 | Journal of Computational Mathematics2018，36，5： | 0 |
| 6 | PENALTY-FACTOR-FREE STABILIZED NONCONFORMING FINITE ELEMENTS FOR SOLVING STATIONARY NAVIER-STOKES EQUATIONS显示文摘Two nonconforming penalty methods for the two-dimensional stationary Navier-Stokes equations are studied in this paper.These methods are based on the weakly continuous P1 vector fields and the locally divergence-free(LDF)finite elements,which respectively penalize local divergence and are discontinuous across edges.These methods have no penalty factors and avoid solving the saddle-point problems.The existence and uniqueness of the velocity solution are proved,and the optimal error estimates of the energy norms and L^(2)-norms are obtained.Moreover,we propose unified pressure recovery algorithms and prove the optimal error estimates of L^(2)-norm for pressure.We design a unified iterative method for numerical experiments to verify the correctness of the theoretical analysis. | Linshuang He Minfu Feng Qiang Ma | 2022 | Journal of Computational Mathematics2022，40，5： | 0 |
| 7 | A C^0-WEAK GALERKIN FINITE ELEMENT METHOD FOR THE TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS IN STREAM-FUNCTION FORMULATION显示文摘We propose and analyze a C^0-weak Galerkin(WG)finite element method for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows.Using a st ream-function formulation,the system of Navier-Stokes equations is reduced to a single fourth-order nonlinear partial differential equation and the incompressibility constraint is automatically satisfied.The proposed method uses continuous piecewisepolynomial approximations of degree k+2 for the stream-function 0 and discontinuous piecewise-polynomial approximations of degreek+1 for the trace of V-0 on the interelement boundaries.The existence of a discrete solution is proved by means of a topological degree argument,while the uniqueness is obtained under a data smallness condition.An optimal error estimate is obtained in L^2-norm,H^1-norm and brokenH^2-norm.Numerical tests are presented to demonstrate the theoretical results. | Baiju Zhang Yan Yang Minfu Feng | 2020 | Journal of Computational Mathematics2020，38，2： | 0 |
| 8 | A Weak Galerkin Mixed Finite Element Method for AcousticWave Equation显示文摘This paper is concerned with the weak Galerkin mixed finite element method(WG-MFEM)for the second-order hyperbolic acoustic wave equation in velocity-pressure formulation.In this formulation,the original second-order differential equation in time and space is reduced to first-order differential equations by introducing the velocity and pressure variables.We employ the usual discontinuous piecewise-polynomials of degree k0 for the pressure and k+1 for the velocity.Furthermore,the normal component of the pressure on the interface of elements is enhanced by polynomials of degree k+1.The time derivative is approximated by the backward Euler difference.We show the stability of the semi-discrete and fullydiscrete schemes,and obtain the suboptimal order error estimates for the velocity and pressure variables.Numerical experiment confirms our theoretical analysis. | Xi Zhang Minfu Feng | 2022 | Advances in Applied Mathematics and Mechanics2022，14，4： | 0 |
| 9 | Stabilized Finite Element Methods for Biot’s Consolidation Problems Using Equal Order Elements显示文摘Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems,the pressure close to the initial time produces large non-physical oscillations.In this paper,we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations.Optimal error estimates for the approximation of displacements and pressure at every time level are obtained,which are valid even close to the initial time.Numerical experiments illustrate and confirm our theoretical analysis. | Gang Chen Minfu Feng | 2018 | Advances in Applied Mathematics and Mechanics2018，10，1： | 0 |
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