A new analysis of discontinuous Galerkin methods for a fourth order variational inequality

Cui Jintao; Zhang Yi

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A new analysis of discontinuous Galerkin methods for a fourth order variational inequality

机译：第四阶变分不等式的不连续Galerkin方法的新分析

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摘要

We study a family of discontinuous Galerkin methods for the displacement obstacle problem of Kirchhoff plates on two and three dimensional convex polyhedral domains, which are characterized as fourth order elliptic variational inequalities of the first kind. We prove that the error in an H-2 -like energy norm is O(h(alpha)) for the quadratic method, where alpha is an element of(1/2, 1] is determined by the geometry of the domain. Under additional assumptions on the contact set such that the solution has improved regularity, we derive the optimal error estimate with alpha is an element of (1, 3/2) for the cubic method. Numerical experiments demonstrate the performance of the methods and confirm the theoretical results. (C) 2019 Elsevier B.V. All rights reserved.

机译：我们研究了一系列不连续的Galerkin方法，用于两个和三维凸多面体结构域的柯希夫板的位移障碍物问题，其特征是第一类的第四阶椭圆变异不等式。我们证明了H-2-Like能量标准中的误差是用于二次方法的O（H（alpha）），其中alpha是由域的几何形状确定的（1/2,1]的元素。在联系人集中的额外假设使得解决方案具有改进的规则性，我们推导出与alpha的最佳误差估计是立方方法的（1,3/2）的元素。数值实验证明了方法的性能并确认理论并确认理论结果。（c）2019年Elsevier BV保留所有权利。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2019年第jul1期|531-547|共17页
作者
Cui Jintao; Zhang Yi;
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作者单位

Hong Kong Polytech Univ Dept Appl Math Hung Hom Hong Kong Peoples R China;

Univ North Carolina Greensboro Greensboro NC 27402 USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Displacement obstacle; Fourth order variational inequality; Discontinuous Galerkin methods; Error estimate;

机译：位移障碍;第四阶变分不等式;不连续的Galerkin方法;错误估计;

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专利

1. A new analysis of discontinuous Galerkin methods for a fourth order variational inequality [J] . Cui Jintao, Zhang Yi Computer Methods in Applied Mechanics and Engineering . 2019,第JULa1期

机译：四阶变分不等式的不连续Galerkin方法的新分析
2. A C-0 interior penalty discontinuous Galerkin method for fourth-order total variation flow. I: Derivation of the method and numerical results [J] . Bhandari Chandi, Hoppe Ronald H. W., Kumar Rahul Numerical Methods for Partial Differential Equations: An International Journal . 2019,第4期

机译：C-0内部惩罚不连续的Galerkin方法，用于四阶总变化流量。 I：衍生方法和数值结果
3. A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality [J] . Wang Fei, Shah Sheheryar, Xiao Wenqiang BIT numerical mathematics . 2021,第3期

机译：用于准分隔不等式的不连续Galerkin方法的先验误差估计
4. A LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE FOURTH-ORDER NLS EQUATION [C] . Wenting Li, Mingchen Yao, Kun Jiang, ICCCI 2010;International conference on computer and computational intelligence . 2010

机译：四阶NLS方程的局部不连续Galerkin方法
5. Efficient Discontinuous Galerkin (DG) Methods for Time-dependent Fourth Order Problems [D] . Yin, Peimeng. 2019

机译：有效的不连续的Galerkin（DG）用于时间依赖性的第四阶问题的方法
6. Comparison of reduced models for blood flow using Runge–Kutta discontinuous Galerkin methods [O] . Charles Puelz, Sunčica Čanić, Béatrice Rivière, -1

机译：使用Runge-Kutta不连续Galerkin方法简化的血流模型的比较
7. A C 0 interior penalty discontinuous Galerkin method for fourth‐order total variation flow. I: Derivation of the method and numerical results [O] . Chandi Bhandari, Ronald H.W. Hoppe, Rahul Kumar 2019

机译：C 0内部惩罚不连续的Galerkin方法，用于四阶总变化流量。 I：衍生方法和数值结果
8. L2 Stability Analysis of the Central Discontinuous Galerkin Method and a Comparison between the Central and Regular Discontinuous Galerkin Methods [R] . Liu, Y. , Shu, C. , Tadmor, E. , 2002

机译：中心间断Galerkin方法的L2稳定性分析及中间与常规间断Galerkin方法的比较

A new analysis of discontinuous Galerkin methods for a fourth order variational inequality

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