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A Well-Conditioned, nonconforming Nitsche’s Extended finite element Method for Elliptic Interface Problems

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Numerical Mathematics(Theory,Methods and Applications) 2020年第1期13卷 99-130页

作者： Xiaoxiao He Fei Song Weibing Deng Department of Mathematics Nanjing UniversityNanjing 210093JiangsuChina Department of Applied Mathematics Nanjing Forestry UniversityNanjing 210037JiangsuChina

In this paper,we introduce a nonconforming Nitsche’s extended finite element method(NXFEM)for elliptic interface problems on unfitted triangulation *** solution on each side of the interface is separately expanded in the standard nonconforming piecewise linear polynomials with the edge averages as degrees of *** jump conditions on the interface and the discontinuities on the cut edges(the segment of edges cut by the interface)are weakly enforced by the Nitsche’s *** the method,the harmonic weighted fluxes are used and the extra stabilization terms on the interface edges and cut edges are added to guarantee the stability and the well *** prove that the convergence order of the errors in energy and L 2 norms are ***,the errors are independent of the position of the interface relative to the mesh and the ratio of the discontinuous ***,we prove that the condition number of the system matrix is independent of the interface *** examples are given to confirm the theoretical results.

关键词： Elliptic interface problems NXFEM nonconforming finite element condition number

nonconforming stabilized combined finite element method for Reissner-Mindlin plate

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Applied Mathematics and Mechanics(English Edition) 2009年第2期30卷 197-207页

作者：冯民富杨艳周天孝 College of Mathematics Sichuan University School of Sciences Southwest Petroleum University Institute of Aeronautical Computing Techniques

Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Numerical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes.

关键词： Reissner-Mindlin plate energy-compatibility combined FEM nonconforming finite element

A Modified nonconforming 5-Node Quadrilateral Transition finite element

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Advances in Applied Mathematics and Mechanics 2010年第6期2卷 784-797页

作者： Feiteng Huang Xiaoping Xie School of Mathematics Sichuan UniversityChengdu 610064China

This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson *** element was originally proposed by Choi and Park[Computers and Structures,32(1989),pp.295–304 and Thin-Walled Structures,28(1997),pp.1–20]for the analysis of Mindlin *** show the consistency error of this element is only O(h^(1/2))over the transition edges of the quadrilateral *** modifying the shape functions with respect to mid-nodes,we get an improved version of the element for which the consistency error is O(h).Numerical examples are provided to verify the theoretical results.

关键词： nonconforming finite element transition element consistency error

AN ERROR ANALYSIS METHOD SPP-BEAM AND A CONSTRUCTION GUIDELINE OF nonconforming finite elementS FOR FOURTH ORDER ELLIPTIC PROBLEMS

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Journal of Computational Mathematics 2020年第1期38卷 195-222页

作者： Jun Hu Shangyou Zhang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA

Under two hypotheses of nonconforming finite elements of fourth order elliptic problems,we present a side-patchwise projection based error analysis method(SPP-BEAM for short).Such a method is able to avoid both the regularity condition of exact solutions in the classical error analysis method and the complicated bubble function technique in the recent medius error analysis *** addition,it is universal enough to admit ***,we propose a sufficient condition for these hypotheses by imposing a set of in some sense necessary degrees of freedom of the shape function *** an application,we use the theory to design a P3 second order triangular H2 non-conforming element by enriching two P4 bubble functions and,another P4 second order triangular H2 nonconforming finite element,and a P3 second order tetrahedral H2 non-conforming element by enriching eight P4 bubble functions,adding some more degrees of freedom.

关键词： nonconforming finite element A priori error analysis Biharmonic equation

EXPLICIT ERROR ESTIMATES FOR MIXED AND nonconforming finite elementS

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Journal of Computational Mathematics 2009年第4期27卷 425-440页

作者： Shipeng Mao Zhong-ci Shi LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex- tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.

关键词： Mixed finite element nonconforming finite element Explicit error estimate,Maximal angle condition.

A NOTE ON THE nonconforming finite elementS FOR ELLIPTIC PROBLEMS

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Journal of Computational Mathematics 2011年第2期29卷 215-226页

作者： Boran Gao Shuo Zhang Ming Wang School of Mathematical Sciences Peking University Beijing 100871 China ICMSEC AMSS Chinese Academy of Science Beijing 100190 PR China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, a class of rectangular finite elements for 2m-th-oder elliptic boundary value problems in n-dimension （m, n ≥1） is proposed in a canonical fashion, which includes the （2m - 1）-th Hermite interpolation element （n = 1）, the n-linear finite element （m = 1） and the Adini element （m = 2）. A nonconforming triangular finite element for the plate bending problem, with convergent order （O（h2）, is also proposed.

关键词： nonconforming finite element Elliptic boundary value problem Plate bending problem.

High accuracy nonconforming finite elements for fourth order problems

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Science China Mathematics 2012年第10期55卷 2183-2192页

作者： WANG Ming ZU PengHe ZHANG Shuo LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China LSEC ICMSEC and NCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The approach of nonconforming finite element method admits users to solve the partial differential equations with lower complexity,but the accuracy is usually *** this paper,we present a family of highaccuracy nonconforming finite element methods for fourth order problems in arbitrary *** finite element methods are given in a unified way with respect to the *** is an effort to reveal the balance between the accuracy and the complexity of finite element methods.

关键词： fourth order problem nonconforming finite element high accuracy arbitrary dimensions

曲边区域上非线性双曲积分微分方程的非协调有限元方法

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高等学校计算数学学报 2013年第3期35卷 222-232页

作者：张步英陈绍春河北科技师范学院欧美学院郑州大学数学系

1引言曲边区域上的各类问题研究由于其更加切合研究的实际情况,引起了各界学者的广泛讨论.本文考虑下列曲边区域上的非线性双曲积分微分方程:其中Ω（?）R;为有界区域,其边界（?）Ω=Γ是C;光滑的,T>0且各系数满足如下条件A:（Ⅰ）(?)a;... 详细信息

1引言曲边区域上的各类问题研究由于其更加切合研究的实际情况,引起了各界学者的广泛讨论.本文考虑下列曲边区域上的非线性双曲积分微分方程:其中Ω（?）R;为有界区域,其边界（?）Ω=Γ是C;光滑的,T>0且各系数满足如下条件A:（Ⅰ）(?)a;,a;>0使得0

关键词： nonconforming finite element nonlinear hyperbolic integrodifferential equations domains with curved boundaries optimal error estimates

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粘弹性方程的一个二阶非协调有限元逼近分析

高等学校计算数学学报 2013年第3期35卷 240-249页

作者：彭玉成华沛河南省信阳师范学院数学与信息科学学院河南省河南城建学院数理系

1引言有限元方法是古典变分方法与分片多项式插值相结合的产物,由***于1943年首先提出用有限元方法处理偏微分方程的近似解.自上世纪五十年代,计算机技术的迅速发展使得有限元方法取得了长足的进展,现在有限元方法已被工程师和科学家们... 详细信息

1引言有限元方法是古典变分方法与分片多项式插值相结合的产物,由***于1943年首先提出用有限元方法处理偏微分方程的近似解.自上世纪五十年代,计算机技术的迅速发展使得有限元方法取得了长足的进展,现在有限元方法已被工程师和科学家们公认是一种完善的和方便的数值分析工具.经过世界各国广大科技工作者的共同努力,已构造

关键词： Viscoelasticity type equations nonconforming finite element error estimation