问题变分不等式的一类各向异性Crouzeix-Raviart型有限元逼近

本文研究了Signorini变分不等式问题的一类各向异性Crouzeix-Raviart型非协调有限元逼近。通过一些新的技巧,得到了相应的最优误差估计。     

ACCURACY ENHANCEMENT FOR THE SIGNORINI PROBLEM WITH FINITE ELEMENT METHOD

In this paper,we study the accuracy enhancement for the frictionless Signorini problem on a polygonal domain with linear finite elements.Numerical test is given to verify our result.     

问题变分不等式的一类各向异性Crouzeix-Raviartart型有限元逼近

本文研究了Signorini变分不等式问题的一类各向异性Crouzeix-Raviart型非协调有限元逼近。通过一些新的技巧，得到了相应的最优误差估计。     

各向异性非内积型网格下旋转Q1元的收敛性

主要研究非协调旋转Q₁元在各向异性非内积型网格,即各向异性平行四边形网格下的收敛性．该元的插值误差在各向异性网格剖分时是发散的,但是我们证明了它对于二阶椭圆问题的各向异性收敛性．为了克服该元插值误差的这个缺陷,构造了一个适当的算子来证明它的逼近性质．利用一定的分析技巧,在各向异性平行四边形网格剖分下,得到了旋转Q₁元的最优逼近误差和相容误差．该结果可以引发人们继续分析一些不满足各向异性插值性质单元的收敛性．文章的最后用一些算例来验证了理论分析的正确性．     

三维Stokes问题各向异性混合元分析

本文提出了一个一般的立方体单元格式并将其应用到三维Stokes问题的混合有限元逼近,给出了各向异性插值误差估计,相容误差估计和LBB条件成立的验证,从而证明了其在不满足正则性和拟一致条件下的收敛性．另外我们还得到了其一个特殊收敛性质,即在解(u,p)∈(H3(Ω))3×H2(Ω)时,相容误差阶为O(h2max),比插值误差阶O(hmax)高一阶．     

New second order nonconforming triangular element for planar elasticity problems

In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn’s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn’s second inequality holds and the convergence order is two.     

A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM

The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value prob-lem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L2-norms are independent of the Lame parameterλ.