Stokes型积分-微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法

在半离散格式下.研究了Stokes型积分一微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法,在不需要传统Ritz-Volterra投影下,通过辅助空间等新的技巧得到了与传统有限元方法相同的误差估计.     

非定常Stokes问题的矩形Crouzeix-Raviart型各向异性非协调元变网格方法

该文给出了关于速度-压力型非定常Stokes问题的一个 矩形 Crouzeix-Raviart 型各向异性非协调有限元的变网格逼近格式.并用一些新的技巧和方法导出了各向异性网格下的有关速度和压力的最优误差估计.     

一个Crouzeix-Raviart型有限元方法关于二阶椭圆问题超逼近的一个新证明

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.     

二阶椭圆问题的稳定化杂交有限元分析

0　引　　言Raviart&Thomas(1977)[13]基于Babǔska-Brezzi有限元理论[1][5]发展了二阶椭圆问题的基本杂交方法.该文指出,为确定合适的自由度,一般将杂交元刻划为非协调元.然而,对三角形偶数次杂交元和四边形杂交元而言,[13]是通过扩充手段克服有限维空间“匹配”问题的.由于扩充元的复杂性及其不再能刻划为非协调元,以致于实际计算无法选取自由度.Thomas的博士论文[15]提供了一个解决办法.即利用Gauss-Legendre数值求积分公式将扩充元近似刻划成非协调元,得到数值积分意义下的杂交方法.如此处理虽然大大简化了原杂交格式的求解过程,但数…     

Sobolev方程的一类各向异性非协调有限元逼近

在各向异性网格下,分别讨论了Sobolev方程在半离散和全离散格式下的一类非协调有限元逼近,得到了与传统有限元方法相同的误差估计和一些超逼近性质.同时在半离散格式下,通过构造具有各向异性特征的插值后处理算子得到了整体超收敛结果.     

非单调型拟线性椭圆问题的非协调元逼近

用非协调有限元来研究非单调型拟线性椭圆问题,使用Aubin-Nitsche对偶技巧,给出了在范数‖.‖h和‖.‖0下的最优误差估计.     

二阶椭圆问题的混合有限元估计

关于二阶椭圆问题，[1]中给出了一种混合有限格式，但所用的自由度太多，给实     

非协调元逼近非单调型拟线性椭圆问题的超收敛分析

研究了非协调有限元逼近非单调型拟线性椭圆问题,使用超收敛误差估计技巧,得出该问题光滑解和有限元解之间存在的超收敛关系.     

特征值问题的Lagrange型各向异性有限元方法

在各向异性网格下首先研究了二阶椭圆特征值问题算子谱逼近的若干抽象结果.然后将这些结果具体应用于线性和双线性Lagrange型协调有限元,得到了与传统有限元网格剖分下相同的最优误差估计,从而拓宽了已有的成果.     

双曲型方程的非协调变网格有限元方法

采用变网格的思想讨论了双曲型方程在各向异性网格下的Crouzeix-Raviart型非协调有限元逼近.在不需要引入传统分析中Riesz投影的情况下,得到了相应最优误差估计.     

三维各向异性非协调Carey有限元的收敛性分析

In this paper, the convergence analysis of the famous Carey element in 3-D is studied on anisotropic meshes. The optimal error estimate is obtained based on some novel techniques and approach, which extends its applications.     

各向异性网格下抛物方程一个新的非协调混合元收敛性分析

本文将 Crouzeix-Raviart 型非协调线性三角形元应用到抛物方程,建立了一个新的混合元格式.在抛弃传统有限元分析的必要工具 Ritz 投影算子的前提下,直接利用单元的插值性质和导数转移技巧, 分别得到了各向异性剖分下关于原始变量u 的H^-1-模和积分意义下L²-模以及通量p=-▽u 在L²-模下的最优阶误差估计.数值结果与我们的理论分析是相吻合的.     

各向异性网格下具有数值积分的非协调有限元逼近

In this paper we mainly discuss the nonconforming finite element method for second order elliptic boundary value problems on anisotropic meshes.By changing the discretization form(i.e.,by use of numerical quadrature in the procedure of computing the left load),we obtain the optimal estimate O(h),which is as same as in the traditional finite element analysis when the load f∈H~1(Ω)∩C~0(Ω)which is weaker than the previous studies.The results obtained in this paper are also valid to the conforming triangular element and nonconforming Carey's element.     

Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition _K/h_K c₀ > 0 is not satisfied, whereh_K is the diameter of the element K and _K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L²-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek.     

A nonconforming mixed finite element for second-order elliptic problems

In a recent work, Hiptmair [Mathematisches Institut, M9404, 1994] has constructed and analyzed a family of nonconforming mixed finite elements for second-order elliptic problems. However, his analysis does not work on the lowest order elements. In this article, we show that it is possible to construct a nonconforming mixed finite element for the lowest order case. We prove the convergence and give estimates of optimal order for this finite element. Our proof is based on the use of the properties of the so-called nonconforming bubble function to control the consistency terms introduced by the nonconforming approximation. We further establish an equivalence between this mixed finite element and the nonconforming piecewise quadratic finite element of Fortin and Soulie [J. Numer. Methods Eng., 19, 505–520, 1983]. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 445–457, 1997     

四阶椭圆方程的一个十六参数能量正交四面体元(英文)

In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions.The newly constructed element is proved to be convergent for a model biharmonic equation.     

双曲积分微分方程的各向异性非协调有限元逼近

讨论了双曲积分微分方程在半离散格式下的一类各向异性非协调有限元逼近,得到了与传统有限元方法相同的最优误差估计和超逼近性质.同时利用插值后处理技术得到了整体超收敛结果.