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1.
非定常Navier-Stokes方程的稳定化特征有限元法 总被引:1,自引:0,他引:1
1引言特征线有限元法是求解对流扩散问题的有效方法。在处理对流占优问题时,表现出了很好的稳定性[8]。对于求解Navier-Stokes方程,文[9]建立了特征有限元格式,并进行了详细分析,但得到的收敛阶O(h~m △t (h~(m 1)/△t))只是拟丰满的。文[10]对此作了非线性稳定性的进一步分析,给出了关于速度和压力的最优误差估计。但目前所有的特征有限元法都要求有限元空间满足inf-sup条件,这就排除了工程实际应用计算方便的低阶有 相似文献
2.
分析了Rd,d=2,3维不可压缩流Stokes问题低次元稳定有限体积方法,它主要利用局部压力投影方法对两种流行但不满足inf-sup条件的有限元配对(P_1-P_0和P_1-P_1)在有限体积方法的框架下进行稳定;利用有限元与有限体积方法的等价性进行有限体积方法理论分析.结果表明不可压缩流Stokes问题在f∈Hd,d=2,3维不可压缩流Stokes问题低次元稳定有限体积方法,它主要利用局部压力投影方法对两种流行但不满足inf-sup条件的有限元配对(P_1-P_0和P_1-P_1)在有限体积方法的框架下进行稳定;利用有限元与有限体积方法的等价性进行有限体积方法理论分析.结果表明不可压缩流Stokes问题在f∈H1情况下,本文方法得到的解与稳定有限元方法解之间具有O(h1情况下,本文方法得到的解与稳定有限元方法解之间具有O(h2)阶超收敛阶结果,且稳定有限体积方法取得了与稳定有限元方法相同的收敛速度,与稳定有限元方法比较,稳定有限体积方法计算简单高效,同时保持物理守恒,因此在实际应用中具有很好的潜力。 相似文献
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Jason S. Howell 《Journal of Computational and Applied Mathematics》2009,231(2):780-792
In this work a finite element method for a dual-mixed approximation of Stokes and nonlinear Stokes problems is studied. The dual-mixed structure, which yields a twofold saddle point problem, arises in a formulation of this problem through the introduction of unknown variables with relevant physical meaning. The method approximates the velocity, its gradient, and the total stress tensor, but avoids the explicit computation of the pressure, which can be recovered through a simple postprocessing technique. This method improves an existing approach for these problems and uses Raviart-Thomas elements and discontinuous piecewise polynomials for approximating the unknowns. Existence, uniqueness, and error results for the method are given, and numerical experiments that exhibit the reduced computational cost of this approach are presented. 相似文献
5.
Hou-De Han 《计算数学(英文版)》1987,5(2):135-143
In this paper, a new finite element scheme for Navier-Stokes equations is proposed, in which three different partitions (in the two dimensional case) are used to construct finite element subspaces of the velocity field and the pressure. The error estimate of the finite element than approximation is given. The precision of this new scheme has the same order as the scheme $Q_2/P_0$, but it is more economical that the scheme $Q_2/P_0$. 相似文献
6.
Hong-xing Rui 《应用数学学报(英文版)》2005,21(3):359-372
Finite volume element method for the Stokes problem is considered. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H^1 norm error estimate. For two widely used dual meshes we give the L^2 norm error estimates, which is optimal in one case and quasi-optimal in another ease. Finally we give a numerical example. 相似文献
7.
《中国科学 数学(英文版)》2017,(8)
This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1(k 0) and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k + 1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results. 相似文献
8.
将求解不可压缩流动的旋度形式压力校正格式从Stokes方程延拓到非定常不可压缩Navier-Stokes方程.在第一步需要求解一个线性的对流-扩散方程,在第二步求解一个Stokes问题.首先给出格式的稳定性分析,然后采用P_2—P_1元分别使用标准形式的压力校正格式和旋度形式的压力校正格式进行了数值模拟,模拟结果表明,对于速度的L~2,H~1误差,两种格式几乎一样,对于压力的L~2误差,旋度形式的压力校正格式略有改进. 相似文献
9.
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 CrouzeixRaviart 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. 相似文献
10.
芮洪兴 《数学物理学报(B辑英文版)》2004,24(1):129-138
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H^1 norm error estimates are given. 相似文献
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对非定常线性化Navier-Stokes方程提出了非协调流线扩散有限元方法.用向后Euler格式离散时间,用流线扩散法处理扩散项带来的非稳定性.速度采用不连续的分片线性逼近,压力采用分片常数逼近.得到了离散解的存在唯一性以及在一定范数意义下离散解的稳定性和误差估计. 相似文献
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Yaqin Jiang 《高等学校计算数学学报(英文版)》2007,16(4):328-340
In this paper,we propose a mortar element method with Lagrange multiplier for incompressible Stokes problem,i.e.,the matching constraints of velocity on mortar edges are expressed in terms of Lagrange multipliers.We also present P_1 noncon- forming element attached to the subdomains.By proving inf-sup condition,we derive optimal error estimates for velocity and pressure.Moreover,we obtain satisfactory approximation for normal derivatives of the velocity across the interfaces. 相似文献
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Li likang 《数学年刊B辑(英文版)》1987,8(1):43-55
There are many papers in which approximate solution of Navier-Stokes problem is discussed by finite element method. Their error estimates are optimal, but degree of piecewise polynomials for pressure p or degree of piecewise polynomials for velocity u are not the lowest. In this papre a new element is given. Its degre for p and degree for u are the lowest and error estimates are optimal. 相似文献
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1. IntroductionIn the numerical approximation of PDE, it is often very importals to detect regionswhere the accuracy of the numerical solution is degraded by local singularities of the solutionof the continuous problem such as the singularity near the re-entrant corller. An obviousremedy is to refine the discretization in the critical regions, i.e., to place more gridpointswhere the solution is less regular. The question is how to identify these regions automdticallyand how to determine a goo… 相似文献
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Xianmin Xu 《计算数学(英文版)》2023,41(2):191-210
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the continuous one. This enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise polynomials. We show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to infinity. The global minimizer, once it is detected by the discrete scheme, approximates the continuous stationary solution in optimal order. Numerical examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results. 相似文献
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设Ω?R~2是有界区域,边界为?Ω。考虑定常Stokes方程: -γ△u+?p=f,在Ω内, divu=0, 在Ω内,(1.1) u=0, 在?Ω上,其中γ>0是常数,u代表流体速度,p为压力,f为已知的外力。这是流体力学中常见的方程,它的混合变分形式为:求u∈[H_0~1(Ω)]~2,p∈L_0~2(Ω)满足 相似文献
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Nonconforming mixed finite element approximation to the stationary Navier-Stokes equations on anisotropic meshes 总被引:1,自引:0,他引:1
The main aim of this paper is to study the error estimates of a rectangular nonconforming finite element for the stationary Navier-Stokes equations under anisotropic meshes. That is, the nonconforming rectangular element is taken as approximation space for the velocity and the piecewise constant element for the pressure. The convergence analysis is presented and the optimal error estimates both in a broken H1-norm for the velocity and in an L2-norm for the pressure are derived on anisotropic meshes. 相似文献
19.
Shuangshuang Chen Xiaoli Li Hongxing Rui 《Numerical Methods for Partial Differential Equations》2019,35(5):1904-1927
In this paper, we present and analyze a finite volume method based on the Crouzeix–Raviart element for the coupled fracture model, where the fluid flow is governed by Darcy's law in the one‐dimensional fracture and two‐dimensional surrounding matrix. In the numerical scheme, the pressure in the matrix and fracture is respectively approximated by the Crouzeix–Raviart elements and piecewise constant functions, and then the velocity is calculated by piecewise constant functions element by element. The existence and uniqueness of the numerical solution are discussed, and optimal order error estimates for both the pressure p and the velocity u are proved on general triangulations. We finally carry out numerical experiments, and results confirm our theoretical analysis. 相似文献
20.
Lois Mansfield 《Numerische Mathematik》1984,45(2):165-172
Summary Optimal rates of convergence for the approximate solution of the stationary Stokes equations are obtained for finite element schemes which use piecewise constants to approximate the pressure and piecewise linear or piecewise bilinear or trilinear polynomials to approximate the velocity over fairly general quadrilateral or hexahedral meshes.This research was supported by NSF Grant MC80-16532 相似文献