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Related papers: Robust block preconditioners for poroelasticity

200 papers

We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified…

Numerical Analysis · Mathematics 2025-07-22 Wietse M. Boon , Xiaozhe Hu , Xue Wang

In this manuscript we focus on the question: what is the correct notion of Stokes-Biot stability? Stokes-Biot stable discretizations have been introduced, independently by several authors, as a means of discretizing Biot's equations of…

Numerical Analysis · Mathematics 2021-04-19 Kent-Andre Mardal , Marie E. Rognes , Travis B. Thompson

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…

Numerical Analysis · Mathematics 2018-03-09 D. Jodlbauer , U. Langer , T. Wick

A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…

Numerical Analysis · Mathematics 2022-05-25 Andrea Franceschini , Laura Gazzola , Massimiliano Ferronato

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

We construct and analyze a preconditioner of the linear elastiity system discretized by conforming linear finite elements in the framework of the auxiliary space method. The auxiliary space preconditioner is based on discretization of a…

Numerical Analysis · Mathematics 2010-03-15 James Brannick , Durkbin Cho

In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…

Numerical Analysis · Mathematics 2022-02-10 Timo Heister , Katrin Mang , Thomas Wick

We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…

Numerical Analysis · Mathematics 2023-07-19 Martina Bukac , Ivan Yotov , Rana Zakerzadeh , Paolo Zunino

Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and…

Numerical Analysis · Mathematics 2025-04-25 Michele Botti , Daniele Prada , Anna Scotti , Michele Visinoni

We propose a new finite element method for the three-field formulation of Biot's consolidation model in poroelasticity and prove a priori error estimates. Uniform-in-time error estimates of all the unknowns are obtained for both…

Numerical Analysis · Mathematics 2014-04-17 Jeonghun J. Lee

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…

Numerical Analysis · Mathematics 2023-06-27 Wietse M. Boon , Martin Hornkjøl , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a structure-preserving finite-element approximation with…

Numerical Analysis · Mathematics 2016-05-03 James H. Adler , Xiaozhe Hu , Ludmil T. Zikatanov

We consider the system of partial differential equations stemming from the time discretization of the two-field formulation of the Biot's model with the backward Euler scheme. A typical difficulty encountered in the space discretization of…

Numerical Analysis · Mathematics 2020-08-13 A. Khan , P. Zanotti

We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…

Numerical Analysis · Mathematics 2025-09-25 Sabit Mahmood Khan , Yashar Mehmani

We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been…

Numerical Analysis · Mathematics 2020-01-01 Herbert Egger , Mania Sabouri

In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…

Numerical Analysis · Mathematics 2016-09-23 Lorenz Berger

This work investigates inexact block Schur complement preconditioning for linear poroelasticity problems discretized using a hybrid approach: Bernardi-Raugel elements for solid displacement and lowest-order weak Galerkin elements for fluid…

Numerical Analysis · Mathematics 2025-12-25 Weizhang Huang , Zhuoran Wang

We propose four-field and five-field Hu--Washizu-type mixed formulations for nonlinear poroelasticity -- a coupled fluid diffusion and solid deformation process -- considering that the permeability depends on a linear combination between…

Numerical Analysis · Mathematics 2025-02-20 Bishnu P. Lamichhane , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled…

Numerical Analysis · Mathematics 2021-08-10 Matteo Frigo , Nicola Castelletto , Massimiliano Ferronato