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We present a priori error analysis for a fully discrete, parallelizable, explicit loosely coupled scheme for the time-dependent Stokes-Biot problem. The method decouples the fluid and poroelastic subproblems in a fully explicit fashion,…

Numerical Analysis · Mathematics 2026-03-24 Yifan Wang , Jeonghun Lee , Suncica Canic

This paper is concerned with numerical algorithms for Biot model. By introducing an intermediate variable, the classical 2-field Biot model is written into a 3-field formulation. Based on such a 3-field formulation, we propose a coupled…

Numerical Analysis · Mathematics 2022-04-19 Huipeng Gu , Mingchao Cai , Jingzhi Li

This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…

Numerical Analysis · Mathematics 2024-01-08 Francesco Ballarin , Sanghyun Lee , Son-Young Yi

In this paper we present and analyze a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a flow in a poroelastic medium. The flows are governed by the Stokes and Biot equations,…

Numerical Analysis · Mathematics 2021-05-25 Sergio Caucao , Tongtong Li , Ivan Yotov

In this work, we consider a fully dynamic Biot model that includes memory effects due to evolving permeability. Time integrals are used to account for the change in structure. We propose an iterative splitting scheme for this model,…

Numerical Analysis · Mathematics 2024-07-24 Jakob S. Stokke , Morten Jakobsen , Kundan Kumar , Florin A. Radu

In this paper, we consider partitioned numerical methods for quasi-static multiple-network poroelasticity (MPET) equations, generalizations of the Biot model in poroelasticity for multiple pore networks. Two partitioned numerical methods…

Numerical Analysis · Mathematics 2024-12-20 Jeonghun J. Lee

We perform a convergence analysis of a two-grid staggered solution algorithm for the Biot system modeling coupled flow and deformation in heterogeneous poroelastic media. The algorithm first solves the flow subproblem on a fine grid using a…

Numerical Analysis · Mathematics 2018-10-24 Saumik Dana , Mary F Wheeler

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the…

Numerical Analysis · Mathematics 2024-02-19 Ryan M. Aronson , Nicola Castelletto , François P. Hamon , J. A. White , Hamdi A. Tchelepi

This work extends the hydro-mechanical phase-field fracture model to non-isothermal conditions with micromechanics based poroelasticity, which degrades Biot's coefficient not only with the phase-field variable (damage) but also with the…

Numerical Analysis · Mathematics 2024-04-25 Yuhao Liu , Keita Yoshioka , Tao You , Hanzhang Li , Fengshou Zhang

Multilayered poroelastic structures are found in many biological tissues such as cartilage and the cornea, and play a key role in the design of bioartificial organs and other bioengineering applications. Motivated by these applications, we…

Numerical Analysis · Mathematics 2025-07-15 Andrew Scharf , Martina Bukač , Sunčica Čanić

In this work, semi-discrete and fully-discrete error estimates are derived for the Biot's consolidation model described using a three-field finite element formulation. The fields include displacements, total stress and pressure. The model…

Numerical Analysis · Mathematics 2020-08-05 Wenya Qi , Padmanabhan Seshaiyer , Junping Wang

Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable.…

Numerical Analysis · Mathematics 2025-03-12 R. Altmann , M. Deiml

We study the fully mixed formulation of the Biot equations, which is characterized by a symmetric coupling between flow and deformation. This structure enables the use of stable mixed finite elements for each subproblem without a strong…

Numerical Analysis · Mathematics 2026-03-20 Fleurianne Bertrand , Jakub Wiktor Both , Tugay Dağlı

This paper presents a study of solution strategies for the Cahn-Hilliard-Biot equations, a complex mathematical model for understanding flow in deformable porous media with changing solid phases. Solving the Cahn-Hilliard-Biot system poses…

Numerical Analysis · Mathematics 2024-01-25 Erlend Storvik , Cedric Riethmüller , Jakub Wiktor Both , Florin Adrian Radu

This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative…

Numerical Analysis · Mathematics 2018-10-11 Saumik Dana , Mary F. Wheeler

We consider the dynamic Biot model describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a saturated porous medium. The model couples a hyperbolic…

Numerical Analysis · Mathematics 2024-01-10 Johannes Kraus , Maria Lymbery , Kevin Osthues , Fadi Philo

We develop and analyze a splitting method for fluid-poroelastic structure interaction. The fluid is described using the Stokes equations and the poroelastic structure is described using the Biot equations. The transmission conditions on the…

Numerical Analysis · Mathematics 2024-09-30 Aashi Dalal , Rebecca Durst , Annalisa Quaini , Ivan Yotov

This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled…

Numerical Analysis · Mathematics 2025-07-29 Jijing Zhao , Huangxin Chen , Mingchao Cai , Shuyu Sun

We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed…

Numerical Analysis · Mathematics 2016-06-23 Jeonghun J. Lee

In this work, we develop Crank-Nicolson-type iterative decoupled algorithms for a three-field formulation of Biot's consolidation model using total pressure. We begin by constructing an equivalent fully implicit coupled algorithm using the…

Numerical Analysis · Mathematics 2024-09-30 Huipeng Gu , Mingchao Cai , Jingzhi Li