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- W2951909736 abstract "Abstract 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." @default.
- W2951909736 created "2019-06-27" @default.
- W2951909736 creator A5006596455 @default.
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- W2951909736 date "2022-02-09" @default.
- W2951909736 modified "2023-09-29" @default.
- W2951909736 title "Finite Element Systems for Vector Bundles: Elasticity and Curvature" @default.
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- W2951909736 doi "https://doi.org/10.1007/s10208-022-09555-x" @default.
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