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  

AN ABSTRACT STA BILIZATION METHOD WITH APPLICATIONS TO NONLINEAR INCOMPRESSIBLE ELASTICITY

作　　者：洪庆国 刘春梅 许进超 Hong Qingguo;Liu Chunmei;Xu Jinchao(Department of Mathematics,Pennsylvania State University,Unverisity Park,PA 16802,USA;College of Science,Hunan University of Science and Engineering,Yongzhou 425199,China)

机构地区：[1]宾夕法尼亚州立大学数学系,美国宾州PA16802 [2]湖南科技学院理学院,永州425199

出　　处：《计算数学》2020年第3期298-309,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.11901189);湖南省教育厅科研项目(No.19A191)支持;partially supported by Center for Computational Mathematics and Applications,The Pennsylvania State University。

摘　　要：针对非线性不可压缩弹性力学问题.本文提出了一种抽象的稳定化方法并将其应用于非线性不可压缩弹性问题上.在该框架中,我们证明了只要连续的混合问题是稳定的,则可以修正任何满足离散inf-sup条件的混合有限元方法使其是稳定的且最优收敛的.我们将这种抽象的稳定化理论框架应用于非线性不可压缩弹性力学问题,给出了稳定性和收敛性理论结论,并通过数值实验验证了该结论.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.

关 键 词：非线性不可压缩弹性问题.混合有限元方法 稳定性 

分 类 号：O343[理学—固体力学]