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We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also referred to as MPET models. The focus of the paper is on the…

Numerical Analysis · Mathematics 2019-04-01 Qingguo Hong , Johannes Kraus , Maria Lymbery , Mary Fanett Wheeler

Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a…

Numerical Analysis · Mathematics 2022-09-20 Seshadri R. Basava , Winnifried Wollner

We establish the a-priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models. We consider state based peridynamic models where the force at a material point is due to both the strain between…

Numerical Analysis · Mathematics 2019-03-05 Prashant K. Jha , Robert Lipton

A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are…

Numerical Analysis · Mathematics 2016-05-03 Xiaozhe Hu , Carmen Rodrigo , Francisco J. Gaspar , Ludmil T. Zikatanov

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

Numerical Analysis · Mathematics 2017-10-24 Yujie Liu , Junping Wang , Qingsong Zou

We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…

Numerical Analysis · Mathematics 2026-04-09 Erik Burman , Peter Hansbo , Mats G. Larson , Karl Larsson , Shantiram Mahata

Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…

Numerical Analysis · Mathematics 2023-05-24 Gabriel R. Barrenechea , Volker John , Petr Knobloch

This paper presents the implementation of the eXtended Finite Element Method (XFEM) in the general-purpose commercial software package COMSOL Multiphysics for multi-field thermo-hydro-mechanical problems in discontinuous porous media. To…

Mathematical Software · Computer Science 2021-12-23 Ahmad Jafari , Mohammad Vahab , Pooyan Broumand , Nasser Khalili

Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…

Fluid Dynamics · Physics 2023-06-30 Matilde Fiori , Satyajit Pramanik , Christopher W. MacMinn

In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are…

Numerical Analysis · Mathematics 2024-01-01 Johannes Kraus , Kundan Kumar , Maria Lymbery , Florin Adrian Radu

We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…

Numerical Analysis · Mathematics 2024-02-07 Constantin Bacuta , Daniel Hayes , Tyler O'Grady

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…

Numerical Analysis · Mathematics 2014-03-04 Joerg Grande , Maxim Olshanskii , Arnold Reusken

We investigate a coupled hyperbolic-parabolic system modeling thermoelastic diffusion (resp. thermo-poroelasticity) in plates, consisting of a fourth-order hyperbolic partial differential equation for plate deflection and two second-order…

Numerical Analysis · Mathematics 2025-06-18 Neela Nataraj , Ricardo Ruiz-Baier , Aamir Yousuf

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

Numerical Analysis · Mathematics 2026-04-28 Andrea Bonito , Vivette Girault , Diane Guignard

We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where…

Analysis of PDEs · Mathematics 2011-04-06 Serge Nicaise , Xenophontos Christos

In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…

Numerical Analysis · Mathematics 2026-02-11 Harald Garcke , Robert Nürnberg , Dennis Trautwein

We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass…

Numerical Analysis · Mathematics 2021-12-16 Tongtong Li , Ivan Yotov

We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…

Numerical Analysis · Mathematics 2023-02-16 Constantin Bacuta , Daniel Hayes , Tyler O'Grady

This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The…

Numerical Analysis · Mathematics 2023-12-05 Paola F. Antonietti , Michele Botti , Ilario Mazzieri

We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…

Materials Science · Physics 2020-06-24 Rajat Arora , Xiaohan Zhang , Amit Acharya