An Eigenvalue Problem in Poromechanics
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The multiphysics coupling of fluids and the deformation of porous materials, referred to as poromechanics, is an indispensable component of various applications within, e.g., geotechnical, and biomedical engineering. Poromechanics models usually have a strongly coupled, potentially highly nonlinear character, often with different scales required to be considered. The robustness and reliability of the corresponding numerical approximations as well as efficient solver technologies are therefore essential (see [1]). In this study, we introduce an eigenvalue problem associated with the Biot equations that can be, for instance, the subject of a modal analysis (see, e.g., [2]) of poromechanics models. We approximate the solution to the novel eigenproblem by a finite element methodology. A key aspect of our analysis is the focus on the robustness of the method with respect to the model parameters involved. REFERENCES [1] F. Bertrand, A. Ern, F. Radu, Robust and reliable finite element methods in poromechanics, Computers & Mathematics with Applications, 91 (2021) 1-2. [2] R. Codina, Ö. Türk, Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method, Finite Elements in Analysis and Design, 206 (2022) 103760.