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三维矩形域上泊松方程四面体线元的超逼近与外推 总被引:2,自引:1,他引:1
改进三角元的积分恒等式,使之适用于拟一致四面体元,借此证明了泊松方程四面体线元梯度有超逼近现象,函数值Richardson外推可以提高精度. 相似文献
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椭圆型方程四面体线元的超逼近与外推 总被引:1,自引:0,他引:1
重新讨论了三角线元的积分恒等式,使之适用于三维区域的拟一致四面体元,借此证明了椭圆型方程有限元解梯度有超逼近现象,函数值Richardson外推可以提高精度. 相似文献
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粘弹性方程各向异性有限元方法的超收敛分析 总被引:2,自引:0,他引:2
克服了传统有限元要求剖分网格满足正则假设(或拟一致假设)的限制,在一种新定义的各向异性网格———广义拟一致网格上,分析了粘弹性方程双线性有限元解的超逼近性质,并给出相应的超收敛结果。 相似文献
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In this paper,a new proof of superclose of a Crouzeix-Raviart type finite element is given for second order elliptic boundary value problem by Bramble-Hilbert lemma on anisotropic meshes. 相似文献
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The Wilson finite element method is considered to solve a class of twodimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis. 相似文献
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Dongyang Shi Hongbo Guan Wei Gong 《Mathematical Methods in the Applied Sciences》2014,37(8):1130-1136
A low order characteristic‐nonconforming finite element method is proposed for solving a two‐dimensional convection‐dominated transport problem. On the basis of the distinguish property of element, that is, the consistency error can be estimated as order O(h2), one order higher than that of its interpolation error, the superclose result in broken energy norm is derived for the fully discrete scheme. In the process, we use the interpolation operator instead of the so‐called elliptic projection, which is an indispensable tool in the traditional finite element analysis. Furthermore, the global superconvergence is obtained by using the interpolated postprocessing technique. Lastly, some numerical experiments are provided to verify our theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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讨论了四阶非线性双曲方程在半离散格式下的非协调有限元逼近,借助ACM单元的非协调性,得到了最优误差估计,超逼近和超收敛结果.同时利用Bramble-Hilbert引理,构造了一个新的合适的外推格式,得到了比通常收敛性高一阶的超收敛结果. 相似文献
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导出了不完全双二次元的几个积分展开式,并利用这些积分展开式及插值后处理技巧,对Poisson方程得到了比通常误差估计高一阶的超逼近性质和整体超收敛结果. 相似文献
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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