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Least‐squares mixed finite element schemes are formulated to solve the evolutionary Navier‐Stokes equations and the convergence is analyzed. We recast the Navier‐Stokes equations as a first‐order system by introducing a vorticity flux variable, and show that a least‐squares principle based on L2 norms applied to this system yields optimal discretization error estimates. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 441–453, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10015 相似文献
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Yang Liu Hong Li Jinfeng Wang Siriguleng He 《Numerical Methods for Partial Differential Equations》2012,28(2):670-688
Splitting positive definite mixed finite element (SPDMFE) methods are discussed for a class of second‐order pseudo‐hyperbolic equations. Depending on the physical quantities of interest, two methods are proposed. Error estimates are derived for both semidiscrete and fully discrete schemes. The existence and uniqueness for semidiscrete schemes are proved. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 670–688, 2012 相似文献
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Suh‐Yuh Yang 《Numerical Methods for Partial Differential Equations》2002,18(6):738-751
In this article we apply the subdomain‐Galerkin/least squares method, which is first proposed by Chang and Gunzburger for first‐order elliptic systems without reaction terms in the plane, to solve second‐order non‐selfadjoint elliptic problems in two‐ and three‐dimensional bounded domains with triangular or tetrahedral regular triangulations. This method can be viewed as a combination of a direct cell vertex finite volume discretization step and an algebraic least‐squares minimization step in which the pressure is approximated by piecewise linear elements and the flux by the lowest order Raviart‐Thomas space. This combined approach has the advantages of both finite volume and least‐squares methods. Among other things, the combined method is not subject to the Ladyzhenskaya‐Babus?ka‐Brezzi condition, and the resulting linear system is symmetric and positive definite. An optimal error estimate in the H1(Ω) × H(div; Ω) norm is derived. An equivalent residual‐type a posteriori error estimator is also given. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 738–751, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10030. 相似文献
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广义神经传播方程的非协调混合有限元方法 总被引：1，自引：0，他引：1
讨论了广义神经传播方程的一个低阶非协调混合有限元方法,在不引入广义椭圆投影的情况下,直接利用插值技巧,得到了相应的未知函数的最优误差估计. 相似文献
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In this article, we construct an a posteriori error estimator for expanded mixed hybrid finite‐element methods for second‐order elliptic problems. An a posteriori error analysis yields reliable and efficient estimate based on residuals. Several numerical examples are presented to show the effectivity of our error indicators. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 330–349, 2007 相似文献
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In this paper,a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The 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 H1-norm and L2-norm for velocity as well as the L2-norm for the pressure are derived. 相似文献
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Haitao Che Zhaojie Zhou Ziwen Jiang Yiju Wang 《Numerical Methods for Partial Differential Equations》2013,29(3):799-817
H1‐Galerkin mixed finite element method combined with expanded mixed element method is discussed for nonlinear pseudo‐parabolic integro‐differential equations. We conduct theoretical analysis to study the existence and uniqueness of numerical solutions to the discrete scheme. A priori error estimates are derived for the unknown function, gradient function, and flux. Numerical example is presented to illustrate the effectiveness of the proposed scheme. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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本文用H1-Galerkin混合有限元法分析了基于带有记忆项的多孔介质中的对流问题的数学模型,即双曲型积分微分方程．我们得到了在一维情况下函数和它梯度的最优阶误差估计, 并且由此推广到二维和三维情况下,得到了和用传统的混合元方法相同的收敛阶数,而且不用验证满足LBB相容性条件． 相似文献
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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
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Tianliang Hou 《Applicable analysis》2013,92(8):1655-1665
In this article, we analyse a posteriori error estimates of mixed finite element discretizations for linear parabolic equations. The space discretization is done using the order λ?≥?1 Raviart–Thomas mixed finite elements, whereas the time discretization is based on discontinuous Galerkin (DG) methods (r?≥?1). Using the duality argument, we derive a posteriori l ∞(L 2) error estimates for the scalar function, assuming that only the underlying mesh is static. 相似文献
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对热传导方程提出了一个新的H~1-Galerkin非协调混合有限元格式,其逼近空间不需满足LBB相容性条件,且在不引进传统的Rutz投影的情况下,得到了与以往协调有限元方法相同的L~2-模和H~1-模的误差估计. 相似文献
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Christine Bernardi;Frédéric Hecht;Rüdiger Verfürth 《Mathematical Modelling and Numerical Analysis》2009,43(6):1185-1201
We consider a variational formulation of the three-dimensional Navier–Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish a priori and a posteriori error estimates.https://doi.org/10.1051/m2an/2009035 相似文献
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电报方程H~1-Galerkin非协调混合有限元分析 总被引：2，自引：3，他引：2
主要研究一类电报方程的H~1-Galerkin非协调混合有限元方法,在任意四边形网格剖分下,其逼近空间分别取为类Wilson元与双线性Q_1元,在不需要满足LBB相容性条件及不采用传统的Ritz投影的情况下,得到了与常规有限元方法相同的L~2-模和H~1-模的误差估计,进一步拓展了H~1-Galerkin混合有限元和类Wilson元的应用范围. 相似文献
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Thinh T. Kieu 《Numerical Methods for Partial Differential Equations》2016,32(1):60-85
The nonlinear Forchheimer equations are used to describe the dynamics of fluid flows in porous media when Darcy's law is not applicable. In this article, we consider the generalized Forchheimer flows for slightly compressible fluids, and then study the expanded mixed finite element method applied to the initial boundary value problem for the resulting degenerate parabolic equation for pressure. The bounds for the solutions, time derivative, and gradient of solutions are established. Utilizing the monotonicity properties of Forchheimer equation and boundedness of solutions, a priori error estimates for solution are obtained in ‐norm, ‐norm as well as for its gradient in ‐norm for all . Optimal ‐error estimates are shown for solutions under some additional regularity assumptions. Numerical results using the lowest order Raviart–Thomas mixed element confirm the theoretical analysis regarding convergence rates. Published 2015. Numer Methods Partial Differential Eq 32: 60–85, 2016 相似文献
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Interior estimates are proved in the L ∞ norm for stable finite element discretizations of the Stokes equations on translation invariant meshes. These estimates yield information about the quality of the finite element solution in subdomains a positive distance from the boundary. While they have been established for second-order elliptic problems, these interior, or local, maximum norm estimates for the Stokes equations are new. By applying finite differenciation methods on a translation invariant mesh, we obtain optimal convergence rates in the mesh size h in the maximum norm. These results can be used for analyzing superconvergence in finite element methods for the Stokes equations. 相似文献
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Ailing Zhu Tingting Xu Qiang Xu 《Numerical Methods for Partial Differential Equations》2016,32(5):1357-1377
The semidiscrete and fully discrete weak Galerkin finite element schemes for the linear parabolic integro‐differential equations are proposed. Optimal order error estimates are established for the corresponding numerical approximations in both and norms. Numerical experiments illustrating the error behaviors are provided.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1357–1377, 2016 相似文献
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An a posteriori error analysis for Boussinesq equations is derived in this article. Then we compare this new estimate with a previous one developed for a regularized version of Boussinesq equations in a previous work. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 214–236, 2000 相似文献
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张铁 《高等学校计算数学学报(英文版)》2000,(2)
l introductionho Paper is the second part of our work on the Ritz-Volterra projection and its applicationS. In the ho Pot['7, we have aide a systematic study on the stability and approximationprO~ Of RitZ-Volterra theectioo in ac and L, spaces for 2igloo. In this paper, as acplications Of Ritz-Volterra projection, we wb investigate the sealliscrete finite element approtoations to initial-boUndary value problems Of varys evolution equations such as parabolicand hyperbolic integral-differe… 相似文献