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崔明 《高等学校计算数学学报》2002,24(3):206-211
1 引 言设Ω R2为具有光滑边界的有界区域,考虑非定常的,无量纲化的,而且带有热传导的粘性不可压缩流体力学问题:问题(Ⅰ):求u=(u1,u2),p,T满足: 相似文献
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本文讨论了一个角形区域上边界条件有间断点的Laplace方程混合边值问题 的适定性,并给出了完整的解答. 相似文献
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特征值问题混合有限元法的一个误差估计 总被引:3,自引:0,他引:3
设(λh,σh,uh)是一个混合有限元特征对.Babuska和Osborn建立了(λh,uh)的误差估计.本文导出了σh的抽象误差估计式.并把该估计式应用于二阶椭圆特征值问题Raviart-Thomas混合有限元格式和重调和算子特征值问题Ciarlet-Raviart混合有限元格式,得到了一些新的误差估计. 相似文献
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混合有限元法的误差分析 总被引:1,自引:0,他引:1
关于混合变分问题有限元方法的研究工作,见[1]—[4].其中已得出混合法的最优误差估计.本文讨论抽象混合有限元法的误差并证明一些超收敛估计,然后将其应用到具体问题上,即应用到一个四阶边值问题和一个二阶边值问题. 相似文献
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本文通过所谓的速度-压力型公式讨论了Navier-Stokes方程的变网格非协调有限元逼近,得到了在确定模意义下的速度、压力误差估计,且在一定条件下,某些误差估计能达到最优。 相似文献
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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。 相似文献
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In this article, we propose a new finite element space Λ$_h$ for the expanded mixed finite element method (EMFEM) for second-order elliptic problems to guarantee its computing capability and reduce the computation cost. The new finite element space Λ$_h$ is designed in such a way that the strong requirement V$_h\subset$Λ$_h$ in [9] is weakened to {v$_h\in$V$_h$; divv$_h$=0}$\subset$Λ$_h$ so that it needs fewer degrees of freedom than its classical counterpart. Furthermore, the new Λ$_h$ coupled with the Raviart-Thomas space satisfies the inf-sup condition, which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix, and thus the existence, uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in $\mathbb{R}^d, d=2,3$ and for triangular partitions in $\mathbb{R}^2$. Also, the solvability of the EMFEM for triangular partition in $\mathbb{R}^3$ can be directly proved without the inf-sup condition. Numerical experiments are conducted to confirm these theoretical findings. 相似文献
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Zhen-Dong Luo 《计算数学(英文版)》2000,18(5):449-456
In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate. 相似文献
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本文.我们给出三维空间的Navier-Stokes问题的一种新的六面体单元的混合有限元格式. 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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伪双曲方程的新混合有限元方法 总被引:1,自引:1,他引:1
构造分析一类二阶伪双曲方程的H1-Galerkin扩展混合有限元方法,该方法采用了扩展混合有限元方法和H1-Galerkin混合有限元方法相结合的技巧.新的格式同时保持了扩展混合有限元方法和H1-Galerkin混合有限元方法的优点.该混合格式与标准的混合格式相比能同时逼近三个变量:未知函数、梯度和流量(系数乘以梯度),并且不必满足LBB相容性条件. 相似文献
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A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem
Hanzhang Hu & Yanping Chen 《计算数学(英文版)》2022,40(5):794-813
A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the $L^q$ error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective. 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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利用修正的H~1-Galerkin混合有限元方法研究了广义神经传播方程,论证了其半离散解的存在唯一性,得到了半离散解的最优阶误差估计,该方法的优点是不需验证LBB相容性条件. 相似文献