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We consider Biot model with block preconditioners and generalized eigenvalue problems for scalability and robustness to parameters. A discontinuous Galerkin discretization is employed with the displacement and Darcy flow flux discretized as…

Numerical Analysis · Mathematics 2023-06-23 Pilhwa Lee

This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…

Numerical Analysis · Mathematics 2025-12-25 Liet Vo

This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…

Numerical Analysis · Mathematics 2026-05-12 Patrick Bammer , Lothar Banz , Miriam Schönauer , Andreas Schröder

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 ${ P_{1}^{c}}\oplus {RT0}-P0$ discretization of the Stokes equations on general simplicial meshes in two/three dimensions (2D/3D), which yields an exactly divergence-free and pressure-independent velocity…

Numerical Analysis · Mathematics 2021-09-07 Xu Li , Hongxing Rui

In this paper, we conduct a numerical analysis of the strong stabilization and polynomial decay of solutions for the initial boundary value problem associated with a system that models the dynamics of a mixture of two rigid solids with…

Numerical Analysis · Mathematics 2026-03-24 Kais Ammari , Vilmos Komornik , Mauricio Sepúlveda , Octavio Vera

In this work we analyze an optimized artificial fixed-stress iteration scheme for the numerical approximation of the Biot system modelling fluid flow in deformable porous media. The iteration is based on a prescribed constant artificial…

Numerical Analysis · Mathematics 2017-05-24 M. Bause , F. A. Radu , U. Köcher

This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using $C^1$-continuous finite elements constructed from NURBS interpolation. Both displacement-based and…

Computational Engineering, Finance, and Science · Computer Science 2017-01-04 Roger A. Sauer , Thang X. Duong , Kranthi K. Mandadapu , David J. Steigmann

Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) algorithms are developed for a 2D Biot model. The model is formulated with mixed-finite elements as a saddle-point problem. The displacement $\mathbf{u}$ and the Darcy flux…

Numerical Analysis · Mathematics 2023-06-23 Pilhwa Lee

We study cut finite element discretizations of a Darcy interface problem based on the mixed finite element pairs $\textbf{RT}_k\times Q_k$, $k\geq 0$. Here $Q_k$ is the space of discontinuous polynomial functions of degree less or equal to…

Numerical Analysis · Mathematics 2024-01-26 Thomas Frachon , Peter Hansbo , Erik Nilsson , Sara Zahedi

We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to…

Numerical Analysis · Mathematics 2024-07-19 Tameem Almani , Kundan Kumar

We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…

Numerical Analysis · Mathematics 2024-09-13 Manu Jayadharan , Ivan Yotov

In this paper, we develop a new multiphysics finite element method for a nonlinear poroelastic model with Hencky-Mises stress tensor. By introducing some new notations, we reformulate the original model into a fluid-fluid coupling problem,…

Numerical Analysis · Mathematics 2026-02-24 Yanan He , Zhihao Ge

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 analyse a coupled 3D-2D model with a free fluid governed by Stokes flow in the bulk and a poroelastic plate described by the Biot-Kirchhoff equations on the surface. Assuming the form of a double perturbed saddle-point problem, the…

Numerical Analysis · Mathematics 2026-03-11 Franco Dassi , Rekha Khot , Andres E. Rubiano , Ricardo Ruiz-Baier

This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement…

Numerical Analysis · Mathematics 2025-02-25 Jingshi Li , Jiachuan Zhang , Ran Zhang

We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the…

Numerical Analysis · Mathematics 2025-09-24 Costanza Aricò , Rainer Helmig , Ivan Yotov

In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [45]. The discretization is proved to be well-posed with respect to the physical and discretization parameters, and…

Numerical Analysis · Mathematics 2020-01-07 James H. Adler , Francisco J. Gaspar , Xiaozhe Hu , Peter Ohm , Carmen Rodrigo , Ludmil T. Zikatanov

In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…

Numerical Analysis · Mathematics 2026-03-03 Huangxin Chen , Yuxiang Chen , Jisheng Kou , Shuyu Sun

We consider the dynamic Biot model (see [Biot, M. A. J. Appl. Phys. 33, 1482--1498 (1962)]) describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a…

Numerical Analysis · Mathematics 2025-07-29 Johannes Kraus , Maria Lymbery , Kevin Osthues