Mathematical Basis of G Spaces

被引:22
作者
Chen, Meng [1 ]
Li, Ming [1 ]
Liu, G. R. [2 ]
机构
[1] Taiyuan Univ Technol, Coll Math, 79 Yingze West Main St, Taiyuan 030024, Peoples R China
[2] Univ Cincinnati, Sch Aerosp Syst, 2851 Woodside Dr, Cincinnati, OH 45221 USA
基金
中国国家自然科学基金;
关键词
G(s) spaces; weakened weak formulations; smoothed finite element methods; norm equivalence; lower boundedness; convergence; FINITE-ELEMENT-METHOD; POINT INTERPOLATION METHOD; SOLID MECHANICS PROBLEMS; METHOD LC-PIM; TETRAHEDRAL ELEMENTS; VIBRATION ANALYSES; FEM; FORMULATION;
D O I
10.1142/S0219876216410073
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper represents some basic mathematic theories for Gs spaces of functions that can be used for weakened weak (W-2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of Gs spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H-1 spaces. We then prove the equivalence of the Gs norms and its corresponding seminorms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and alpha S-FEM to examine the properties of a smoothed method based on Gs spaces, in comparison with the standard FEM with weak formulation.
引用
收藏
页数:21
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