Finite Element Systems for Vector Bundles: Elasticity and Curvature

Christiansen Snorre H.; Hu Kaibo

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Finite Element Systems for Vector Bundles: Elasticity and Curvature

机译：Finite Element Systems for Vector Bundles: Elasticity and Curvature

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摘要

We develop a theory of finite element systems, for the purpose of discretizing sections of vector bundles, in particular those arising in the theory of elasticity. In the presence of curvature, we prove a discrete Bianchi identity. In the flat case, we prove a de Rham theorem on cohomology groups. We check that some known mixed finite elements for the stress-displacement formulation of elasticity fit our framework. We also define, in dimension two, the first conforming finite element spaces of metrics with good linearized curvature, corresponding to strain tensors with Saint-Venant compatibility conditions. Cochains with coefficients in rigid motions are given a key role in relating continuous and discrete elasticity complexes.

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《Foundations of computational mathematics》 |2023年第2期|545-596|共52页
作者
Christiansen Snorre H.; Hu Kaibo;
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作者单位

Univ Oslo;

Univ Oxford;

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原文格式 PDF
正文语种英语
中图分类应用数学;
关键词
Finite elements; Elasticity; Bianchi identity; de Rham theorem; FREE STOKES ELEMENTS; DIFFERENTIAL FORMS; LINEAR ELASTICITY; EXTERIOR CALCULUS; CONSTRUCTION; COMPLEXES; FAMILY; APPROXIMATION; STABILITY; SMOOTH;

Finite Element Systems for Vector Bundles: Elasticity and Curvature

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