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PENALTY-FACTOR-FREE STABILIZED NONCONFORMING FINITE ELEMENTS FOR SOLVING stationary navier-stokes equations

Journal of Computational Mathematics 2022年第5期40卷 728-755页

作者： Linshuang He Minfu Feng Qiang Ma School of Mathematics Sichuan UniversityChengdu 610064China

Two nonconforming penalty methods for the two-dimensional stationary navier-stokes equations are studied in this *** 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 *** methods have no penalty factors and avoid solving the saddle-point *** existence and uniqueness of the velocity solution are proved,and the optimal error estimates of the energy norms and L^(2)-norms are ***,we propose unified pressure recovery algorithms and prove the optimal error estimates of L^(2)-norm for *** design a unified iterative method for numerical experiments to verify the correctness of the theoretical analysis.

关键词： stationary navier-stokes equations Nonconforming finite elements Penalty stabilization methods DG methods Locally divergence-free.

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A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE stationary navier-stokes equations

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Acta Mathematica Scientia 2011年第2期31卷 367-382页

作者：石东洋任金城龚伟 Department of Mathematics Zhengzhou University Department of Mathematics Shangqiu Normal University Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary navier-stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

关键词： stationary navier-stokes equations nonconforming mixed finite elementscheme optimal order error estimates

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Two-Level Stabilized Finite Volume Methods for the stationary navier-stokes equations

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Advances in Applied Mathematics and Mechanics 2013年第1期5卷 19-35页

作者： Tong Zhang Shunwei Xu School of Mathematics&Information Science Henan Polytechnic UniversityJiaozuo 454003HenanChina

In this work,two-level stabilized finite volume formulations for the 2D steady navier-stokes equations are *** methods are based on the local Gauss integration technique and the lowest equal-order finite element ***,the two-level stabilized finite volume methods involve solving one small navierstokes problem on a coarse mesh with mesh size H,a large general stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size h=O(H^(2))or a large general stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size h=O(|logh|^(1/2)H^(3)).These methods we studied provide an approximate solution(ue v h,pe v h)with the convergence rate of same order as the standard stabilized finite volume method,which involve solving one large nonlinear problem on a fine mesh with mesh size ***,our methods can save a large amount of computational time.

关键词： stationary navier-stokes equations finite volume method two-level method error estimate

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On Partial Regularity of Suitable Weak Solutions to the stationary Fractional navier-stokes equations in Dimension Four and Five

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Acta Mathematica Sinica,English Series 2017年第12期33卷 1632-1646页

作者： Xiao Li GUO Yue Yang MEN Department of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou 450002 P. R. China Institute of Applied Physics and Computational Mathematics Beijing 100088 P. R. China

In this paper, we investigate the partial regularity of suitable weak solutions to the multi- dimensional stationary navier-stokes equations with fractional power of the Laplacian （-△）^α （n/6 ≤α〈1 and a ≠ 1/2）. It is shown that the n ＋ 2 - 6α （3 ≤ n ≤5） dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in ε-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20].

关键词： stationary navier-stokes equations suitable weak solutions partial regularity

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A Second Order Nonconforming Triangular Mixed Finite Element Scheme for the stationary navier-stokes equations

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Chinese Quarterly Journal of Mathematics 2017年第1期32卷 88-98页

作者：王志军郝晓斌石东洋 School of Mathematics and Statistics Zhengzhou Normal UniversityZhengzhou 450044China School of Science Henan Institute of EngineeringZhengzhou 451191China School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450052China

In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary navier-stokes *** new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H^1-norm and L^2-norm for velocity as well as the L^2-norm for the pressure are derived.

关键词： stationary navier-stokes equations nonconforming triangular mixed finite element scheme optimal error estimates

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