Year: 2026
Type: preprint
Abstract: In two and three dimensions, we analyze a mixed formulation of the nonlinear Biot equations in terms of the poroelastic stress tensor, the displacement, the pressure, and the rotation tensor. To establish the well-posedness of the problem, we introduce suitable stabilization terms, leading to an augmented mixed formulation in which the associated parameters are chosen appropriately. Owing to the nonlinearity of the problem, we employ a fixed-point strategy to prove the existence and uniqueness of solutions. We propose a finite element scheme for which we establish existence and uniqueness of a discrete solution, together with a priori error estimates. Additionally, we design and analyze an a posteriori error estimator of the residual type which results to be reliable and efficient. Finally, we present a series of numerical experiments in two and three dimensions in order to assess the performance of the proposed method.
Source: arXiv (Cornell University)
Institutions: University of Bío-Bío, Universidad de Los Lagos, Monash University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214898597