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1.
AN ANISOTROPIC NONCONFORMING FINITE ELEMENT WITH SOME SUPERCONVERGENCE RESULTS   总被引:54,自引:0,他引:54  
The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis.  相似文献
2.
石东洋  梁慧 《计算数学》2005,27(4):369-382
本文对二阶椭圆问题构造了一个新的非常规Hermite型矩形单元并用各向异性插值基本定理证明了其各向异性特征,从而可用于任意的矩形剖分.同时还得到了与网格的正则性假设和拟一致假设无关的超逼近和超收敛性质以及外推.数值结果表明该单元确实是一个具有很好应用价值的单元且与理论分析是相吻合的.  相似文献
3.
各向异性网格下Wilson元的超收敛性分析   总被引:3,自引:0,他引:3  
在各向异性网格下研究了二阶椭圆边值问题的Wilson有限元方法,利用单元构造的特殊性和一些新的技巧得到相应的超逼近和超收敛结果.数值算例的结果与理论分析是相吻合的.  相似文献
4.
Stokes问题非协调混合有限元超收敛分析   总被引:1,自引:0,他引:1  
本文通过引入全新的技巧,研究了Stokes问题的非协调混合有限元方法,得到了关于速度与压力的超逼近性质.进一步地通过构造一个恰当的插值后处理算子,还得到了关于速度的整体超收敛结果.  相似文献
5.
李清善  孙会霞 《数学季刊》2007,22(3):388-394
The paper studies the convergence and the superconvergence of the biquadratic finite element for Poisson' problem on anisotropic meshes.By detailed analysis,it shows that the biquadratic finite element is anisotropically superconvergent at four Gauss points in the element.  相似文献
6.
1 Introduction The Wilson nonconforming element has been widely used in computational mechanics and struc- tural engineering because of its good convergence. In many practical cases, it seems better than the bilinear conforming finite element. This phenomenon causes the great interest of many people who study finite elements. Some papers about the Wilson element have been published which deal with superconvergence. In [6], the superclose property and the global superconvergence are obtained …  相似文献
7.
在各向异性网格下,得到了Stokes问题著名的Bernadi-Raugel混合有限元格式的超逼近性质,而且通过构造插值后处理算子得到了关于速度的超收敛结果.  相似文献
8.
EQ rot 1 nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2 ) one order higher than its interpolation error O(h), the superclose results of order O(h2 ) in broken H1 -norm are obtained. At the same time, the global superconvergence in broken H1 -norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4 ) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ rot 1 element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.  相似文献
9.
Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa-tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that (▽h ( u-Ihu )1, ▽hvh) h may be estimated as order O ( h2 ) when u ∈ H3 (Ω), where Ihu denotes the bilinear interpolation of u , vh is a polynomial belongs to quasi-Wilson finite element space and ▽h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O ( h2 ) /O ( h3 ) in broken H 1-norm, which is one/two order higher than its interpolation error when u ∈ H3 (Ω) /H4 (Ω). Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapola- tion result of order O ( h3 ), two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme.  相似文献
10.
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ||·||div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.  相似文献
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