Mixed finite element methods for linear Cosserat equations
CoRR(2024)
摘要
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 weaky 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.
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