Speaker
Nanna Berre,Norwegian University of Science and Technology
Abstract
In this presentation, we introduce cut finite element methods for the numerical solution of Biot’s consolidation model for poroelasticity. This model describes the coupled deformation of an elastic porous medium and the viscous fluid flow within it, making it crucial for applications in geoscience, medicine, and biophysics. These applications often involve domains with complex and intricate geometries, posing significant challenges for generating high-quality volumetric meshes suitable for simulation. To address this issue, we employ unfitted finite element methods, where the domain boundary is represented independently of the background mesh, significantly simplifying the meshing process.
Our approach combines the total pressure formulation from [2, 3] with unfitted finite element techniques [1], resulting in geometrically robust solution schemes. We demonstrate how our formulation enables us to establish stability and derive a priori error estimates comparable to those in [2, 3]. Finally, we present comprehensive numerical results to validate our theoretical findings and discuss the strengths and limitations of the proposed methods, including their robustness with respect to problem parameters.
References
[1] E. Burman, S. Claus, P. Hansbo, M. G. Larson, and A. Massing. CutFEM: discretizing geometry and partial differential equations. Int. J. Numer. Meth. Engng., Vol. 104, pp. 472–501, 2015.
[2] R. Oyarzua, R. Ruiz-Baier, Locking-free finite element methods for poroelasticity. SIAM J. NUMER. ANAL., Vol. 54, No. 5 pp. 2951–2973, 2016.
[3] J. J. Lee, K.-A. Mardal, R. Winther Parameter-robust discretization and preconditioning ofBiot’s consolidation model. SIAM J. SCI. COMPUT., Vol. 39, No. 1 pp. A1-A24, 2016.