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This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…

Numerical Analysis · Mathematics 2022-07-07 Theodore L. Chang , Chin-Long Lee

In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…

Numerical Analysis · Mathematics 2021-12-28 Zhihao Ge , Wenlong He

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

We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject…

Analysis of PDEs · Mathematics 2023-12-22 Thomas Eiter , Katharina Hopf , Robert Lasarzik

In the present work we propose and analyze a fully coupled virtual element method of high order for solving the two dimensional nonstationary Boussinesq system in terms of the stream-function and temperature fields. The discretization for…

Numerical Analysis · Mathematics 2023-03-22 L. Beirão da Veiga , D. Mora , A. Silgado

We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…

Numerical Analysis · Mathematics 2026-03-11 Santiago Badia , Wei Li , Ricardo Ruiz-Baier

The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…

Computational Physics · Physics 2018-06-05 Alexey Y. Chernyshenko , Maxim A. Olshanskii , Yuri V. Vassilevski

In this paper we discuss the application of nonconforming virtual element methods(VEM) for the second order diffusion dominated convection diffusion reaction equation. Stability of the virtual element methods has been proved for the…

Numerical Analysis · Mathematics 2015-12-24 Dibyendu Adak , E. Natarajan

This work considers the application of the virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known…

Numerical Analysis · Mathematics 2020-06-24 Daniel van Huyssteen , Batmanathan Dayanand Reddy

We discuss nonconforming virtual element method for convection dominated (diffusive coefficient is very small compared to convective coefficient and reac- tion coefficient ) convection-diffusion-reaction equation using L^2 projection…

Numerical Analysis · Mathematics 2016-01-07 Dibyendu Adak , E. Natarajan

In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…

Numerical Analysis · Mathematics 2026-02-24 Zhihao Ge , Wenshuai Hu

This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…

Numerical Analysis · Mathematics 2020-02-10 M. Cihan , F. Aldakheel , B. Hudobivnik , P. Wriggers

We develop mixed finite element methods for nonlinear reaction-diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations.…

Numerical Analysis · Mathematics 2023-04-27 Jeonghun J. Lee , Xinran Jin

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced…

Numerical Analysis · Mathematics 2020-12-03 L. Beirão da Veiga , F. Dassi , C. Lovadina , G. Vacca

We present a family of Virtual Element Methods for three-dimensional linear elasticity problems based on the Hellinger-Reissner variational principle. A convergence and stability analysis is developed. Moreover, using the hybridization…

Numerical Analysis · Mathematics 2023-06-01 Michele Visinoni

We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…

Numerical Analysis · Mathematics 2024-06-21 Dennis Trautwein

Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out…

Computational Engineering, Finance, and Science · Computer Science 2020-12-16 Xiang Yu , Yibin Fu , Hui-Hui Dai

We propose mixed finite element methods for Cosserat materials that use suitable quadrature rules to eliminate the Cauchy and coupled stress variables locally. The reduced system consists of only the displacement and rotation variables.…

Numerical Analysis · Mathematics 2025-11-11 Wietse M. Boon , Alessio Fumagalli , Jan M. Nordbotten , Ivan Yotov

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

In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Darcy type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation…

Numerical Analysis · Mathematics 2021-06-08 Mario Alvarez , Eligio Colmenares , Filánder A. Sequeira