This paper proposes a quadrilateral finite element method of the lowest orderfor Reissner-Mindlin (R-M) plates on the basis of Hellinger-Reissner variationalprinciple, which includes variables of displacements, shear stresses and bendingmoments. This method uses continuous piecewise isoparametric bilinear interpolationfor the approximation of transverse displacement and rotation. Thepiecewise-independent shear stress/bending moment approximation is constructedby following a self-equilibrium criterion and a shear-stress-enhanced condition. Apriori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t. Numerical experiments confirm the theoreticalresults.

In this paper, an energy-compatibility condition is used for stress optimization in the derivation of new accurate 8-node hexahedral elements for threedimensional elasticity. Equivalence of the proposed hybrid method to an enhanced strains method is established, which makes it easy to extend the method to general nonlinear problems. Numerical tests show that the resultant elements possess high accuracy at coarse meshes, are insensitive to mesh distortions and free from volume locking in the analysis of beams, plates and shells.

A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming (P1)2-P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.

Based on a weighted average of the modified Hellinger–Reissner principle and its dual, the combined hybrid finite element (CHFE) method was originally proposed with a combination parameter limited in the interval (0, 1). In actual computation this parameter plays an important role in adjusting the energy error of discretization models. In this paper, a novel expression of the combined hybrid variational form is used to show the relationship between the resultant method and some Galerkin/least-squares stabilized finite scheme for plate bending problems. The choice of combination parameter is then extended to (-1, 0) S (0, 1). Existence, uniqueness and convergence of the solution of discrete schemes are proved, and the advantage of the parameter extension in computation is discussed. As an application, improvement of Adini’s rectangular element by the CHFE approach is performed.

In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results.

Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms. One estimator is shown to be reliable and efficient, which yields global upper and lower bounds for the error in piecewise W1,p- seminorm. The other one is proved to give a global upper bound of the error in Lp-norm. By taking the two estimators as refinement indicators, adaptive algorithms are suggested, which are experimentally shown to attain optimal convergence orders.

In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy’s law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zeroth- order term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods are based on the original weak formulations of Darcy-Stokes-Brinkman equations. In the first method we consider the existing Stokes elements. We show that a stable Stokes element is also uniformly stable with respect to the coefficients and the jumps of Darcy-Stokes-Brinkman equations if and only if the discretely divergence-free velocity implies almost everywhere divergence-free one. In the second method we construct uniformly stable elements by modifying some well-known H(div)-conforming elements. We give some new 2D and 3D elements in a unified way. In the last method we modify the original weak formulation of Darcy-Stokes- Brinkman equations with a stabilization term. We show that all traditional stable Stokes elements are uniformly stable with respect to the coefficients and their jumps under this new formulation.

A 4-node hybrid stress quadrilateral element is presented with compatible isoparametric bilinear displacements and a new version of 5-parameter stresses which satisfies both self-equilibrium equations and an energy orthogonal relation between stress terms and Wilson incompatible strains. Based on different element formulations, another two new elements are also derived and shown to be identical to the first element. Numerical benchmark experiments show that the three equivalent elements possess high accuracy at coarse meshes, are frame invariant and free from Poisson locking at the nearly incompressible limit. Since the 5-parameter stress mode used does not have uncoupled constant terms, the elements do not pass the patch test.

从克服Locking发散性到高性能格式的研究发展是过去十年有限元法研究的一个重要方面。本文认为所谓高性能有限元方法是一种特别的低阶位移工，它具有如下的理论和计算优点：（1）保持物理力学问题固有的数学物理特征；（2）因此，应用于工程数值模拟，它是“鲁棒”的、高明效的。按此立场，评论介绍了在计算结构力学和计算流体力学中发展的克服两类Locking发散性的有限方法