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1.
孙萍  罗振东  陈静 《计算数学》2008,30(3):327-336
本文讨论二阶椭圆问题的混合有限元逼近的一种泡函数稳定性,并给出其基于简化的稳定化格式的先验误差估计和后验误差估计.该方法较通常的格式(例如,Raviaxt-Thomas方法的同阶格式)节省大量的自由度.  相似文献
2.
A stabilized mixed finite element formulation for four-noded tetrahedral elements is introduced for robustly solving small and large deformation problems. The uniqueness of the formulation lies within the fact that it is general in that it can be applied to any type of material model without requiring specialized geometric or material parameters. To overcome the problem of volumetric locking, a mixed element formulation that utilizes linear displacement and pressure fields was implemented. The stabilization is provided by enhancing the rate of deformation tensor with a term derived using a bubble function approach. The element was implemented through a user-programmable element of the commercial finite element software ANSYS. Using the ANSYS platform, the performance of the element was evaluated by comparing the predicted results with those obtained using mixed quadratic tetrahedral elements and hexahedral elements with a B-bar formulation. Based on the quality of the results, the new element formulation shows significant potential for use in simulating complex engineering processes.  相似文献
3.
1引言用混合有限元方法求解Stokes问题的近似解时,有两点重要事项.其一是众所周知的稳定化条件,这就导致在一阶及二阶格式中引人水泡(bubble)函数(参见[1],[2],[4]和[6]).其二是在实际计算中,含有体力密度f的积分,需代之以数值积分,而保持原有的逼近阶不变.值得指出的是。该数值积分与水泡(bubble)函数项无关.考虑数值积分下的Stokes问题混合元逼近:设给定空间其中,是有界连通的多边形区域.考虑Stokes问题混合变分形式:求V,p M,使得其中表示L2内积.众所周知,(…  相似文献
4.
本文针对Stokes-问题给出了[12]发展的基于局部bubble-函数稳定化有限元法与Gals-稳定化有限元法,bubble函数扩充元法的等价关系  相似文献
5.
段火元 《应用数学》1998,11(2):98-103
本文针对混合结构抽象问题,基于「9」的非标准稳定化有限元方法的一般框架研究了bubble-函数稳定化方法,该逼近代格式使得Babuska-Brezzi条件是不必要的。  相似文献
6.
本文针对形如σu α·u-kΔu=f对流—扩散型的模型问题,发展耦合局部bubble-函数的有限元方法,我们就α=0和σ=0两种情形证明了方法的与“影响因素”σ和pedlet-数无关稳定性及全局最佳收敛阶。  相似文献
7.
针对自由边界条件壳体问题的经典混合变分模型发展局部bubble函数稳定化有限元逼近方法:逐单元附加带嵌入bubble函数的局部双线性型的稳定化法.已证明离散方程具有一致稳定性,从而经典InfSup条件被避免;同时给出最优误差估计  相似文献
8.
1. IntroductionAs far as the shell problem is concerned, [l] established a mixed formulation in the clas-sical W that the K-ellipticity and the lnfSup condition are introduced. Unfortunately it isvery dndcult to construct ndxed elemellts simultaneously satisfying the K-ellipticity and theInfSup conditionI2], which are indeed prerequisites Of the stability and the convergence. Inaddition, the indefiniteness of the resulting linear algebraic system complicates the solutionalgorithIn.ffecentl…  相似文献
9.
本文给出Reissner-Mindlin板问题的线性格式[1]中的汽泡函数的最优选取。  相似文献
10.
We show that existing quadrilateral nonconforming finite elements of higher order exhibit a reduction in the order of approximation if the sequence of meshes is still shape-regular but consists no longer of asymptotically affine equivalent mesh cells. We study second order nonconforming finite elements as members of a new family of higher order approaches which prevent this order reduction. We present a new approach based on the enrichment of the original polynomial space on the reference element by means of nonconforming cell bubble functions which can be removed at the end by static condensation. Optimal estimates of the approximation and consistency error are shown in the case of a Poisson problem which imply an optimal order of the discretization error. Moreover, we discuss the known nonparametric approach to prevent the order reduction in the case of higher order elements, where the basis functions are defined as polynomials on the original mesh cell. Regarding the efficient treatment of the resulting linear discrete systems, we analyze numerically the convergence of the corresponding geometrical multigrid solvers which are based on the canonical full order grid transfer operators. Based on several benchmark configurations, for scalar Poisson problems as well as for the incompressible Navier-Stokes equations (representing the desired application field of these nonconforming finite elements), we demonstrate the high numerical accuracy, flexibility and efficiency of the discussed new approaches which have been successfully implemented in the FeatFlow software (www.featflow.de). The presented results show that the proposed FEM-multigrid combinations (together with discontinuous pressure approximations) appear to be very advantageous candidates for efficient simulation tools, particularly for incompressible flow problems.  相似文献
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