Girault, VivetteGonzález Taboada, MaríaHecht, FrédéricRajagopal, Kumbakonam R.2026-08-182026-08-182026Girault, Vivette, González Taboada, María, Hecht, Frédéric and Rajagopal, Kumbakonam R.. "Error analysis of a BDF2-FEM discretization for flow in deformable porous media" Journal of Numerical Mathematics, 2026. https://doi.org/10.1515/jnma-2025-00251569-3953https://hdl.handle.net/2183/49042[Abstract]: In this work, we consider a linearized model for fluid flow through a deformable porous elastic solid derived using mixture theory. The model accounts for small but non-negligible solid velocity relative to the fluid, resulting in a coupled system of equations. We focus on the error analysis and implementation of two fully discrete schemes: one using the first-order backward Euler method for time discretization and the other employing the second-order BDF2 scheme. We derive error estimates for both procedures and describe numerical experiments on the corresponding non-dimensional system.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Deformable porous mediaFinite element discretizationEuler schemeBDF2 schemeError estimatesNon-dimensional equationsjournal articleopen access10.1515/jnma-2025-0025