References & Citations
Mathematics > Numerical Analysis
Title: Mixed finite element methods for linear Cosserat equations
(Submitted on 22 Mar 2024 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: We consider the equilibrium equations for a linearized Cosserat material. We identify their structure in terms of a differential complex, which is isomorphic to six copies of the de Rham complex through an algebraic isomorphism. Moreover, we show how the Cosserat materials can be analyzed by inheriting results from linearized elasticity. Both perspectives give rise to mixed finite element methods, which we refer to as strongly and weakly coupled, respectively. We prove convergence of both classes of methods, with particular attention to improved convergence rate estimates, and stability in the limit of vanishing Cosserat material parameters. The theoretical results are fully reflected in the actual performance of the methods, as shown by the numerical verifications.
Submission history
From: Omar Duran [view email][v1] Fri, 22 Mar 2024 11:40:26 GMT (3024kb,D)
[v2] Wed, 27 Mar 2024 21:03:40 GMT (2998kb,D)
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