Mixed finite element methods for linear Cosserat equations

• DOI: 10.48550/arxiv.2403.15136
• Publication Date: 2024-03-22
• Authors: Wietse M. Boon; Omar Durán; Jan M. Nordbotten
• Keywords: FOS: Mathematics; 68Q25, 68R10, 68U05; Mathematics - Numerical Analysis; Numerical Analysis (math.NA)

We consider the equilibrium equations for a linearized Cosserat material. identify their structure in terms of differential complex, which is isomorphic to six copies de Rham complex through an algebraic isomorphism. Moreover, we show how materials can be analyzed by inheriting results from elasticity. Both perspectives give rise mixed finite element methods, refer as strongly and weaky coupled, respectively. prove convergence both classes with particular attention improved rate estimates, stability limit vanishing material parameters. The theoretical are fully reflected actual performance shown numerical verifications.