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1.
In this paper, we consider the nonconforming rotated Q
1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral
meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing
another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic
affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements
whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which
coincides with our theoretical analysis. 相似文献
2.
IntroductionQuadrilateral mesh Is widely used In the finite eleme 相似文献
3.
In this paper, we present a posteriori error analysis for the nonconforming Morley element of the fourth order elliptic equation.
We propose a new residual-based a posteriori error estimator and prove its reliability and efficiency. These results refine
those of Beirao da Veiga et al. (Numer Math 106:165–179, 2007) by dropping two edge jump terms in both the energy norm of
the error and the estimator, and those of Wang and Zhang (Local a priori and a posteriori error estimates of finite elements
for biharmonic equation, Research Report, 13, 2006) by showing the efficiency in the sense of Verfürth (A review of a posteriori
error estimation and adaptive mesh-refinement techniques, Wiley-Teubner, New York, 1996). Moreover, the normal component in
the estimators of Beirao da Veiga et al. (Numer Math 106:165–179, 2007) and Wang and Zhang (Local a priori and a posteriori
error estimates of finite elements for biharmonic equation, Research Report, 13, 2006) is dropped, and therefore only the
tangential component of the stress on each edge comes into the estimator. In addition, we generalize these results to three
dimensional case. 相似文献
4.
In this paper, we analyze the convergence of the adaptive conforming and nonconforming $P_1$ finite element methods with red–green refinement based on standard Dörfler marking strategy. Since the mesh after refining is not nested into the one before, the usual Galerkin-orthogonality or quasi-orthogonality for newest vertex bisection does not hold for this case. To overcome such a difficulty, we develop some new quasi-orthogonality instead under certain condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive methods by establishing the reduction of some total errors. To weaken the condition on the initial mesh, we propose a modified red–green refinement and prove the convergence of the associated adaptive methods under a much weaker condition on the initial mesh (Condition B). Furthermore, we also develop an initial mesh generator which guarantee that all the interior triangles are equilateral triangles (satisfy Condition A) and the other triangles containing at least one vertex on the boundary satisfy Condition B. 相似文献
5.
Zhong-ciShi Xue-junXu Hong-yingMan 《计算数学(英文版)》2004,22(6):905-920
In this paper, some effective cascadic multigrid methods are proposed for solving the large scale symmetric or nonsymmetric algebraic systems arising from the finite volume methods for second order elliptic problems. It is shown that these algorithms are optimal in both accuracy and computational complexity. Numerical experiments are reported to support our theory. 相似文献
6.
1.引言设 是Rd(d=2;3)中的有界多角形区域,α是它的边界.考虑下列模型问题此处f∈EL2(Ω),系数AE(C1(Ω))d×d满足下列一致椭园条件此处α0是正常数.此外假设B∈(C1(Ω)d和c∈C0(Ω)([14]).(1.1)式的变分形式是:找u∈H0(Ω)使得最近,非对称不定问题的非协调多重网格法吸引了众多的研究,详见问,[7];[10].考虑非协调元多重网格的一个重要原因是混合元和非协调元之间存在着紧密的联系(详见【几问,问).设FI是fi拟一致的H角形或矩形剖分,是由连接F'-'(… 相似文献
7.
Vibration analysis of Kirchhoff plates is of great importance in many engineering fields. The semi-discrete and the fully discrete Morley element methods are proposed to solve such a problem, which are effective even when the region of interest is irregular. The rigorous error estimates in the energy norm for both methods are established. Some reasonable approaches to choosing the initial functions are given to keep the good convergence rate of the fully discrete method. A number of numerical results are provided to illustrate the computational performance of the method in this paper. 相似文献
8.
We present a new cascadic multigrid for elliptic problems. 相似文献
9.
In this note, by analyzing the interpolation operator of Girault and Raviart given in [V. Girault, P.A. Raviart, Finite element methods for Navier–Stokes equations, Theory and algorithms, in: Springer Series in Computational Mathematics, Springer-Verlag, Berlin,1986] over triangular meshes, we prove optimal interpolation error estimates for Lagrange triangular finite elements of arbitrary order under the maximal angle condition in a unified and simple way. The key estimate is only an application of the Bramble–Hilbert lemma. 相似文献
10.
Shi Zhongci 《数学年刊B辑(英文版)》1990,11(2):148-155
It is observed in practice that the numerical accuracy of the two unconventional plate elements, i. e., the nine parameter quasi-conforming and generalized conforming elements, is better than that of the usual Zienkiewicz in compatible cubic element and of a new element proposed recently by Specht, although all these elements have the same asymptotical rate of convergence O(h) in the energy norm. In the paper a careful error analysis for the quasi-conforming and generalized conforming elements is given. It is shown that the consistency error due to nonconformity of the two unconventional elements is of order O(h~2), one order high than that of other conventional nonconforming elements with nine parameters. 相似文献