English
Related papers

Related papers: Parameter-robust Stochastic Galerkin mixed approxi…

200 papers

We study higher-order space-time variational discretisations for modeling complex processes in porous media that include fluid and structure interactions which are of fundamental importance in many engineering fields with applications in…

Numerical Analysis · Mathematics 2018-05-03 Uwe Köcher , Markus Bause

We focus on the numerical analysis of a polygonal discontinuous Galerkin scheme for the simulation of the exchange of fluid between a deformable saturated poroelastic structure and an adjacent free-flow channel. We specifically address wave…

Numerical Analysis · Mathematics 2025-02-03 Michele Botti , Ivan Fumagalli , Ilario Mazzieri

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

The electroporoelasticity model, which couples Maxwell's equations with Biot's equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on…

Numerical Analysis · Mathematics 2025-02-25 Xuan Liu , Yongkui Zou , Ran Zhang , Yanzhao Cao , Amnon J. Meir

We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear…

Numerical Analysis · Mathematics 2019-02-05 Ilona Ambartsumyan , Vincent J. Ervin , Truong Nguyen , Ivan Yotov

An H(div) conforming finite element method for solving the linear Biot equations is analyzed. Formulations for the standard mixed method are combined with formulation of interior penalty discontinuous Galerkin method to obtain a consistent…

Numerical Analysis · Mathematics 2020-11-17 Beatrice Riviere , Guido Kanschat

In this work, we consider a hybrid mixed finite element method for Biot's model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy's velocity system of Biot's model presented in \cite{C. Niu} is not uniformly stable…

Numerical Analysis · Mathematics 2020-04-28 Chunyan Niu , Hongxing Rui , Xiaozhe Hu

This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytical tool, our method extends to both convex and non-convex…

Numerical Analysis · Mathematics 2024-08-23 Chunmei 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

Modeling flow in geosystems with natural fault is a challenging problem due to low permeability of fault compared to its surrounding porous media. One way to predict the behavior of the flow while taking the effects of fault into account is…

Numerical Analysis · Mathematics 2020-09-11 Youguang Chen , George Biros

We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), and of the four-field formulation of Biot's consolidation…

Numerical Analysis · Mathematics 2020-11-11 Wietse M. Boon , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…

Numerical Analysis · Mathematics 2025-01-09 Hyun Chul Yoon , S. M. Mallikarjunaiah

We present a parameter-robust preconditioner for a hybridizable discontinuous Galerkin (HDG) discretization of a four-field formulation of Biot's consolidation model. We first determine a parameter-robust preconditioner for the full…

Numerical Analysis · Mathematics 2025-08-19 Esteban Henríquez , Jeonghun J. Lee , Sander Rhebergen

In this paper, we propose a new multiphysics finite element method for a Biot model with secondary consolidation in soil dynamics. To better describe the processes of deformation and diffusion underlying in the original model, we…

Numerical Analysis · Mathematics 2022-04-08 Zhihao Ge , Wenlong He

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model partial differential equation, the parameter is given in the…

Numerical Analysis · Mathematics 2026-01-14 Bedřich Sousedík , Kookjin Lee

The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the…

Numerical Analysis · Mathematics 2018-01-17 Eduard Rohan , Vladimír Lukeš

This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists…

Analysis of PDEs · Mathematics 2018-07-05 Mats K. Brun , Elyes Ahmed , Florin A. Radu , Jan Martin Nordbotten

We analyze an iterative coupling of mixed and discontinuous Galerkin methods for numerical modelling of coupled flow and mechanical deformation in porous media. The iteration is based on an optimized fixed-stress split along with a…

Numerical Analysis · Mathematics 2018-02-12 Markus Bause

In this work, we consider the popular P1-RT0-P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation does not satisfy an inf-sup condition uniformly with respect to the…

Numerical Analysis · Mathematics 2018-08-15 Carmen Rodrigo , Xiaozhe Hu , Peter Ohm , James H. Adler , Francisco J. Gaspar , Ludmil Zikatanov

In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium…

Numerical Analysis · Mathematics 2018-04-23 Jeonghun J. Lee , Eleonora Piersanti , Kent-Andre Mardal , Marie E. Rognes