共查询到20条相似文献,搜索用时 31 毫秒
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.
MAO Shipeng & SHI Zhongci Institute of Computational Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences PO Box Beijing China 《中国科学A辑(英文版)》2006,49(10)
In this paper, we consider the nonconforming rotated Q1 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
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In this article, two Morley type non‐C0 nonconforming rectangular finite elements are discussed to numerically solve the fourth order plate bending problem under anisotropic meshes. The optimal anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches. Some numerical tests are given to confirm the theoretical analysis. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
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A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection. 相似文献
8.
Gunar Matthies 《Numerical Algorithms》2001,27(4):317-327
This paper considers finite elements which are defined on hexahedral cells via a reference transformation which is in general trilinear. For affine reference mappings, the necessary and sufficient condition for an interpolation order O(h
k+1) in the L
2-norm and O(h
k
) in the H
1-norm is that the finite dimensional function space on the reference cell contains all polynomials of degree less than or equal to k. The situation changes in the case of a general trilinear reference transformation. We will show that on general meshes the necessary and sufficient condition for an optimal order for the interpolation error is that the space of polynomials of degree less than or equal to k in each variable separately is contained in the function space on the reference cell. Furthermore, we will show that this condition can be weakened on special families of meshes. These families which are obtained by applying usual refinement techniques can be characterized by the asymptotic behaviour of the semi-norms of the reference mapping. 相似文献
9.
A posteriori error estimation for the Stokes–Darcy coupled problem on anisotropic discretization 下载免费PDF全文
Koffi Wilfrid Houedanou Bernardin Ahounou 《Mathematical Methods in the Applied Sciences》2017,40(10):3741-3774
This paper presents an a posteriori error analysis for the stationary Stokes–Darcy coupled problem approximated by finite element methods on anisotropic meshes in or 3. Korn's inequality for piecewise linear vector fields on anisotropic meshes is established and is applied to non‐conforming finite element method. Then the existence and uniqueness of the approximation solution are deduced for non‐conforming case. With the obtained finite element solutions, the error estimators are constructed and based on the residual of model equations plus the stabilization terms. The lower error bound is proved by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence, a so‐called matching function is defined, and its discussion shows it to be useful tool. With its help, the upper error bound is shown by means of the corresponding anisotropic interpolation estimates and a special Helmholtz decomposition in both media. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
Gerd Kunert 《Numerische Mathematik》2000,86(3):471-490
Summary. A new a posteriori residual error estimator is defined and rigorously analysed for anisotropic tetrahedral finite element meshes. All considerations carry over to anisotropic triangular meshes with minor changes only.
The lower error bound is obtained by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence,
a so-called matching function is defined, and its discussion shows it to be a useful tool. With its help anisotropic interpolation estimates and subsequently
the upper error bound are proven. Additionally it is pointed out how to treat Robin boundary conditions in a posteriori error
analysis on isotropic and anisotropic meshes. A numerical example supports the anisotropic error analysis.
Received April 6, 1999 / Revised version received July 2, 1999 / Published online June 8, 2000 相似文献
11.
We study a preconditioner for the boundary element method with high order piecewise polynomials for hypersingular integral equations in three dimensions. The meshes may consist of anisotropic quadrilateral and triangular elements. Our preconditioner is based on an overlapping domain decomposition which is assumed to be locally quasi-uniform. Denoting the subdomain sizes by H
j
and the overlaps by
j
, we prove that the condition number of the preconditioned system is bounded essentially by max
j
O(1+log H
j
/
j
)2. The appearing constant depends linearly on the maximum ratio H
i
/H
j
for neighboring subdomains, but is independent of the elements' aspect ratios. Numerical results supporting our theory are reported. 相似文献
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Ningning Yan 《Advances in Computational Mathematics》2001,15(1-4):333-361
In this paper, we present a posteriori error estimates of gradient recovery type for elliptic obstacle problems. The a posteriori error estimates provide both lower and upper error bounds. It is shown to be equivalent to the discretization error in an energy type norm for general meshes. Furthermore, when the solution is smooth and the mesh is uniform, it is shown to be asymptotically exact. Some numerical results which demonstrate the theoretical results are also reported in this paper. 相似文献
14.
A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRDINGER EQUATION 总被引:1,自引:0,他引:1
In this article, a nonconforming quadrilateral element(named modified quasiWilson element) is applied to solve the nonlinear schr¨odinger equation(NLSE). On the basis of a special character of this element, that is, its consistency error is of order O(h~3) for broken H1-norm on arbitrary quadrilateral meshes, which is two order higher than its interpolation error, the optimal order error estimate and superclose property are obtained. Moreover,the global superconvergence result is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. 相似文献
15.
The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25). 相似文献
16.
In this paper the optimal L
2 error estimates of the finite volume element methods (FVEM) for Poisson equation are discussed on quadrilateral meshes. The
trial function space is taken as isoparametric bilinear finite element space on quadrilateral partition, and the test function
space is defined as piecewise constant space on dual partition. Under the assumption that all elements on quadrilateral meshes
are O(h
2) quasi-parallel quadrilateral elements, we prove convergence rate to be O(h
2) in L
2 norm. 相似文献
17.
Let B denote the unit ball of . For 0<p<∞, the holomorphic function spaces Qp and Qp,0 on the unit ball of are defined as and In this paper, we give some derivative-free, mixture and oscillation characterizations for Qp and Qp,0 spaces in the unit ball of . 相似文献
18.
The main aim of this paper is to have an accurate analysis on the famous Adini's element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini's element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes. 相似文献
19.
GAO Ji-mei LI Wen-hua 《数学季刊》2007,(3)
The main aim of this paper is to have an accurate analysis on the famous Adini's element for the second order problems under to the anisotropic meshes.We firstly show that the interpolation of Adini's element satisfy the anisotropic property.Then the optimal error estimate is obtained without the regularity assumption on the meshes. 相似文献
20.
The largest class of multivalued systems satisfying the module-like axioms is the Hv-module. Hv-modules first were introduced by Vougiouklis. In this paper we define weak equality between two subsets of an Hv-module and introduced the notion of exact sequences of Hv-modules. Also some results on the weak equality and exact sequences are given. 相似文献