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A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…

Numerical Analysis · Mathematics 2018-04-24 Elena Celledoni , Eirik Hoel Høiseth , Nataliya Ramzina

A linear system of differential equations describing a joint motion of thermo-elastic porous body and incompressible thermo-fluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek M. Meirmanov

In this paper, we consider partitioned numerical methods for quasi-static multiple-network poroelasticity (MPET) equations, generalizations of the Biot model in poroelasticity for multiple pore networks. Two partitioned numerical methods…

Numerical Analysis · Mathematics 2024-12-20 Jeonghun J. Lee

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

We present a priori error analysis for a fully discrete, parallelizable, explicit loosely coupled scheme for the time-dependent Stokes-Biot problem. The method decouples the fluid and poroelastic subproblems in a fully explicit fashion,…

Numerical Analysis · Mathematics 2026-03-24 Yifan Wang , Jeonghun Lee , Suncica Canic

In this paper, we consider unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in unsaturated porous media, modeled by a non-linear extension of Biot's quasi-static consolidation model. The coupled, elliptic-parabolic…

Analysis of PDEs · Mathematics 2019-09-17 Jakub Wiktor Both , Iuliu Sorin Pop , Ivan Yotov

In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…

Numerical Analysis · Mathematics 2019-05-22 Nima Noii , Thomas Wick

Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable.…

Numerical Analysis · Mathematics 2025-03-12 R. Altmann , M. Deiml

This paper introduces a unified model for thermo-poroelasticity and multiple-network poroelasticity, reformulated into a total-pressure-based system. We first establish the well-posedness of the problem via a Galerkin-based argument and…

Numerical Analysis · Mathematics 2026-04-01 Huipeng Gu , Mingchao Cai , Jingzhi Li , Yu Jiang

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…

Numerical Analysis · Mathematics 2015-05-13 A. V. Shutov , R. Kreissig

We develop and analyze a splitting method for fluid-poroelastic structure interaction. The fluid is described using the Stokes equations and the poroelastic structure is described using the Biot equations. The transmission conditions on the…

Numerical Analysis · Mathematics 2024-09-30 Aashi Dalal , Rebecca Durst , Annalisa Quaini , 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

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…

Numerical Analysis · Mathematics 2013-12-20 Ulrich Langer , Huidong Yang

In this paper, we propose a multiphysics finite element method for a quasi-static thermo-poroelasticity model with a nonlinear convective transport term. To design some stable numerical methods and reveal the multi-physical processes of…

Numerical Analysis · Mathematics 2023-10-10 Zhihao Ge , Dandan Xu

In this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero-energy modes associated with the original…

Numerical Analysis · Mathematics 2021-03-24 Shashank Menon , Xiaoyu Song

In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2022-01-20 Aleksei Tyrylgin , Maria Vasilyeva , Anatoly Alikhanov , Dongwoo Sheen

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 develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a…

Numerical Analysis · Mathematics 2021-08-04 Manu Jayadharan , Eldar Khattatov , Ivan Yotov

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

In the finite element analysis with fast decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow, we investigate strong nonlinear behavior in 2D creeping contraction flow. The algorithm is applicable in the whole…

Fluid Dynamics · Physics 2011-11-02 Youngdon Kwon