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We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid…

Numerical Analysis · Mathematics 2020-11-30 Jakub W. Both , Nicolas A. Barnafi , Florin A. Radu , Paolo Zunino , Alfio Quarteroni

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes-Darcy model with Beaver-Joseph-Saffman interface condition in literatures, the numerical analysis only get…

Numerical Analysis · Mathematics 2016-02-08 Yanren Hou

We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to…

Computational Engineering, Finance, and Science · Computer Science 2016-01-26 A. E. Kolesov , P. N. Vabishchevich

In this paper, the inherent gradient flow structures of thermo-poro-visco-elastic processes in porous media are examined for the first time. In the first part, a modelling framework is introduced aiming for describing such processes as…

Numerical Analysis · Mathematics 2019-11-27 Jakub Wiktor Both , Kundan Kumar , Jan Martin Nordbotten , Florin Adrian Radu

We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…

Numerical Analysis · Mathematics 2023-12-12 Alessandro Contri , Balázs Kovács , André Massing

We develop a family of mixed finite element methods for a model of nonlinear poroelasticity where, thanks to a rewriting of the constitutive equations, the permeability depends on the total poroelastic stress and on the fluid pressure and…

Numerical Analysis · Mathematics 2025-02-25 Arbaz Khan , Bishnu P. Lamichhane , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

The discretization of fluid-poromechanics systems is typically highly demanding in terms of computational effort. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral…

Numerical Analysis · Mathematics 2024-07-16 Ivan Fumagalli , Nicola Parolini , Marco Verani

We analyze a weak formulation of the coupled problem defining the interac- tion between a free fluid and a poroelastic structure. The problem is fully dynamic and is governed by the time-dependent incompressible Navier-Stokes equations and…

Analysis of PDEs · Mathematics 2022-05-25 Aycil Cesmelioglu

In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted explicit-implicit Euler time integration. We prove that the…

Numerical Analysis · Mathematics 2024-07-18 Aaron Brunk , Marvin Fritz

This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…

Numerical Analysis · Mathematics 2020-04-28 Xiaobing Feng , Hailong Qiu

We propose and analyze a second-order partitioned time-stepping method for a two-phase flow problem in porous media. The algorithm is based on a refactorization of Cauchy's one-leg $\theta$-method. The main part consists of the implicit…

Numerical Analysis · Mathematics 2023-10-10 Giselle Sosa Jones , Catalin Trenchea

We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…

Numerical Analysis · Mathematics 2023-07-19 Carmen Rodrigo , Francisco Gaspar , Xiaozhe Hu , Ludmil Zikatanov

This paper presents and analyzes a fast, robust, efficient, and optimally accurate fully discrete splitting algorithm for the Uncertainty Quantification (UQ) of parameterized Stochastic Navier-Stokes Equations (SNSEs) flow problems those…

Numerical Analysis · Mathematics 2025-02-17 Neethu Suma Raveendran , Md. Abdul Aziz , Sivaguru S. Ravindran , Muhammad Mohebujjaman

In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…

Numerical Analysis · Mathematics 2021-11-01 Asha K Dond , Thirupathi Gudi , Ramesh Ch. Sau

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element…

Numerical Analysis · Mathematics 2025-08-22 Toni Sayah , Toufic El Arwadi

We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…

Numerical Analysis · Mathematics 2026-02-13 Erik Weyl , Andreas Bartel , Manuel Schaller

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…

Numerical Analysis · Mathematics 2018-11-22 Xiaobing Feng , Yukun Li , Yi Zhang

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…

Analysis of PDEs · Mathematics 2014-02-27 Harald Garcke , Michael Hinze , Christian Kahle

This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…

Numerical Analysis · Mathematics 2025-11-03 Krishan Kumar , P. Danumjaya , Anil Kumar , Amiya K. Pani