Continuous finite element methods for Reissner-Mindlin plate problem

On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming (bi)linear macroelements or (bi)quadratic elements, and the rotation by conforming (bi)linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.     

Semi‐analytical integration of the elastic stiffness matrix of an axisymmetric eight‐noded finite element

The finite element method (FEM) is a numerical method for approximate solution of partial differential equations with appropriate boundary conditions. This work describes a methodology for generating the elastic stiffness matrix of an axisymmetric eight‐noded finite element with the help of Computer Algebra Systems. The approach is described as “semi analytical” because the formulation mimics the steps taken using Gaussian numerical integration techniques. The semianalytical subroutines developed herein run 50[percnt] faster than the conventional Gaussian integration approach. The routines, which are made publically available for download,¹ should help FEM researchers and engineers by providing significant reductions of CPU times when dealing with large finite element models. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

电报方程H~1-Galerkin非协调混合有限元分析

主要研究一类电报方程的H~1-Galerkin非协调混合有限元方法,在任意四边形网格剖分下,其逼近空间分别取为类Wilson元与双线性Q_1元,在不需要满足LBB相容性条件及不采用传统的Ritz投影的情况下,得到了与常规有限元方法相同的L~2-模和H~1-模的误差估计,进一步拓展了H~1-Galerkin混合有限元和类Wilson元的应用范围.     

前沿推进曲面四边形网格生成算法

将一类前沿推进三角形曲面网格生成算法拓展到曲面四边形网格生成。新算法逐个单元推进前沿,避免了铺路法（Paving）逐排推进方式的鲁棒性问题,针对四边形算法在理想点计算、候选点列表构建和新单元生成等环节存在的特殊技术问题给出了系统的解决方案。数值实验表明,本文算法能针对复杂的组合参数曲面自动生成全四边形网格,网格质量优于...     

A vertex cover with chorded 4-cycles

Let k be an integer with k ≥ 2 and G a graph with order n > 4k. We prove that if the minimum degree sum of any two nonadjacent vertices is at least n + k, then G contains a vertex cover with exactly k components such that k−1 of them are chorded 4-cycles. The degree condition is sharp in general.     

非结构四边形二次Lagrangian有限元方程的代数多重网格法及收敛性分析

1 引言代数多重网格(AMG)法是求解有结构、非结构冈格下的PDEs离散化系统,以及其它大型稀疏矩阵方程的最为有效的方法之一,是当前多重网格法研究领域的热点．它主要侧重于粗化技术的研究,目前这方面已有大量的工作(见文[1～4]),其中基于部分几何信息和分析信息的AMG法,是当前AMG法发展的一个新趋势(见文[5～7])．     

Nonconforming quadrilateral finite element method for Ginzburg–Landau equation

Nonconforming finite element method is studied for a linearized backward fully-discrete scheme of the Ginzburg–Landau equation with the quadrilateral element. The unconditional convergent result of order O(h + τ) in the broken H¹-norm is deduced rigorously based on a splitting technique, by which the ratio between the subdivision parameter h and the time step τ is removed. Furthermore, numerical results are provided to confirm the theoretical analysis. The analysis developed herein can be regarded as a framework to deal with the unconditional convergent analysis of the Ginzburg–Landau equation for other known low order nonconforming elements.     

定常Satokes方程的窄边四边形有限元法

本文提出了一个试探函数不满足divν＝0的定常Stokes方程的窄边四边形有限元法，利用窄边四边形等参有限元插值定理和Falk的思想，得到了H^1(Ω）模误差的最优收敛估计阶O（h）。     

非正则条件下类Wilson元的构造及其应用

本文在非正则性条件下，研究了窄四边形上的类Wilson元。通过参考元上类Wilson元的构造，证明了由此产生的有限元对任意窄四边形剖分通过Irons分片检查，得到了二阶问题的误差估计。结果表明，该单元的收敛性质与Wilson元的类似。