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 计算数学 2020, Vol. 42 Issue (3): 298-309    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles 1 宾夕法尼亚州立大学数学系, 宾州 PA 16802, 美国;
2 湖南科技学院理学院, 永州 425199
AN ABSTRACT STABILIZATION METHOD WITH APPLICATIONS TO NONLINEAR INCOMPRESSIBLE ELASTICITY
Hong Qingguo1, Liu Chunmei2, Xu Jinchao1
1 Department of Mathematics, Pennsylvania State University, Unverisity Park, PA 16802, USA;
2 College of Science, Hunan University of Science and Engineering, Yongzhou 425199, China
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Abstract： In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element method that satisfies the discrete inf-sup condition can be modified so that it is stable and optimal convergent as long as the mixed continuous problem is stable. Furthermore, we apply the abstract stabilized framework to nonlinear incompressible elasticity problems and present numerical experiments to verify the theoretical results.

 引用本文: . 一种抽象的稳定化方法及在非线性不可压缩弹性问题上的应用[J]. 计算数学, 2020, 42(3): 298-309. . AN ABSTRACT STABILIZATION METHOD WITH APPLICATIONS TO NONLINEAR INCOMPRESSIBLE ELASTICITY[J]. Mathematica Numerica Sinica, 2020, 42(3): 298-309.

  Reddy B, Simo J. Stability and convergence of a class of enhanced strain methods[J]. SIAM J. Numer. Anal., 1995, 32(6):1705-1728. Braess D, Carstensen C, Reddy B. Uniform convergence and a posteriori error estimators for the enhanced strain finite element method[J]. Numer. Math., 2004, 96(3):461-479. Houston P, Schotzau D, Wihler T. An hp-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity[J]. Comput. Methods Appl. Mech. Engrg., 2006, 195(25-28):3224-3246. Hansbo P, Larson M. Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method[J]. Comput. Methods Appl. Mech. Engrg., 2002, 191(17-18):1895-1908. Hong Q, Kraus J, Xu J, Zikatanov L. A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations[J]. Numer. Math., 2016, 132(1):23-49. Wu S, Gong S, Xu J. Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor[J]. Math. Models Methods in Appl. Sci., 2017, 27(14):2711-2743. Gong S, Wu S, Xu J. New hybridized mixed methods for linear elasticity and optimal multilevel solvers[J]. Numer. Math., 2019, 141(2):569-604. Wang F, Wu S, Xu J. A mixed discontinuous Galerkin method for linear elasticity with strongly imposed symmetry[J]. J. Sci. Comput., 2020, 83(1):1-17. Hong Q, Hu J, Ma L, Xu J. An Extended Galerkin Analysis for Linear Elasticity with Strongly Symmetric Stress Tensor[J]. arXiv preprint arXiv:2002.11664, 2020.  Auricchio F, da Veiga L B, Lovadina C, Reali A. A stability study of some mixed finite elements for large deformation elasticity problems[J]. Comput. Methods Appl. Mech. Engrg., 2005, 194(9-11):1075-1092. Wriggers P, Reese S. A note on enhanced strain methods for large deformations[J]. Comput. Methods Appl. Mech. Engrg., 1996, 135(3-4):201-209. Lovadina C, Auricchio F. On the enhanced strain technique for elasticity problems[J]. Comput.& Structures, 2003, 81(8-11):777-787. Pantuso D, Bathe K. On the stability of mixed finite elements in large strain analysis of incompressible solids[J]. Finite Elem. Anal. Des., 1997, 28(2):83-104. Eyck A T, Celiker F, Lew A. Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity:Analytical estimates[J]. Comput. Methods Appl. Mech. Engrg., 2008, 197(33-40):2989-3000. Eyck A T, Celiker F, Lew A. Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity:Motivation, formulation, and numerical examples[J]. Comput. Methods Appl. Mech. Engrg., 2008, 197(45-48):3605-3622. A. Ten Eyck A, Lew A. An adaptive stabilization strategy for enhanced strain methods in nonlinear elasticity[J]. Internat. J. Numer. Methods Engrg., 2010, 81(11):1387-1416.  Auricchio F, da Veiga L B, Lovadina C, Reali A. The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity:mixed FEMs versus NURBS-based approximations[J]. Comput. Methods Appl. Mech. Engrg., 2010, 199(5-8):314-323. Hughes T, Cottrell J, Bazilevs Y. Isogeometric analysis:CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Comput. Methods Appl. Mech. Engrg., 2005, 194(39-41):4135-4195. Brezzi F, Fortin M, Marini L. Mixed Finite Element Methods with Continuous Stresses[J]. Math. Models Methods Appl. Sci., 1993, 3:275-287. Xie X, Xu J, Xue G. Uniformly stable finite element methods for Darcy-Stokes-Brinkman models[J]. J. Comput. Math., 2008, 26(3):437-455.  Bonet J, Wood R. Nonlinear continuum mechanics for finite element analysis[M]. Cambridge University Press, New York, 1997.  Brezzi F, Fortin M. Mixed and hybrid finite element methods[M]. Springer-Verlag, New York, 1991.  Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers[J]. RAIRO Anal. Numer., 1974, 8(2):129-151.  Arnold D, Brezzi F, Fortin M. A stable finite element for the Stokes equations[J]. Calcolo, 1984, 21(4):337-344. Girault V, Raviart P. Finite element methods for Navier-Stokes equations:theory and algorithms[M]. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1986.
  张然. 弱有限元方法在线弹性问题中的应用[J]. 计算数学, 2020, 42(1): 1-17.  关文绘, 曹学年. Riesz回火分数阶平流-扩散方程的隐式中点方法[J]. 计算数学, 2020, 41(1): 42-57.  胡冬冬, 曹学年, 蒋慧灵. 带非线性源项的双侧空间分数阶扩散方程的隐式中点方法[J]. 计算数学, 2019, 41(3): 295-307.  盛秀兰, 赵润苗, 吴宏伟. 二维线性双曲型方程Neumann边值问题的紧交替方向隐格式[J]. 计算数学, 2019, 41(3): 266-294.  杨晋平, 李志强, 闫玉斌. 求解Riesz空间分数阶扩散方程的一种新的数值方法[J]. 计算数学, 2019, 41(2): 170-190.  王俊俊, 李庆富, 石东洋. 非线性抛物方程混合有限元方法的高精度分析[J]. 计算数学, 2019, 41(2): 191-211.  洪旗, 苏帅. 任意四边形网格上扩散问题的一个稳定九点格式[J]. 计算数学, 2019, 40(1): 51-67.  王志强, 文立平, 朱珍民. 时间延迟扩散-波动分数阶微分方程有限差分方法[J]. 计算数学, 2019, 41(1): 82-90.  丛玉豪, 胡洋, 王艳沛. 含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性[J]. 计算数学, 2019, 41(1): 104-112.  丛玉豪, 赵欢欢, 张艳. 中立型时滞微分系统多步龙格-库塔方法的时滞相关稳定性[J]. 计算数学, 2018, 39(4): 310-320.  毛文亭, 张维, 王文强. 一类带乘性噪声随机分数阶微分方程数值方法的弱收敛性与弱稳定性[J]. 计算数学, 2018, 39(3): 161-171.  张根根, 唐蕾, 肖爱国. 求解刚性Volterra延迟积分微分方程的隐显单支方法的稳定性与误差分析[J]. 计算数学, 2018, 40(1): 33-48.  陈丰, 吴峻峰. 分布式通信响应优化问题及其内点法求解[J]. 计算数学, 2017, 39(4): 378-392.  肖飞雁, 李旭旭, 陈飞盛. 非线性延迟积分微分方程连续Runge-Kutta方法的稳定性分析[J]. 计算数学, 2017, 39(1): 1-13.  王涛, 刘铁钢. 求解对流扩散方程的一致四阶紧致格式[J]. 计算数学, 2016, 38(4): 391-404.
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