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We propose and analyze an augmented mixed finite element method for the pseudostress-velocity formulation of the stationary convective Brinkman-Forchheimer problem in $\mathrm{R}^d$, $d\in \{2,3\}$. Since the convective and Forchheimer…

Numerical Analysis · Mathematics 2023-03-03 Sergio Caucao , Johann Esparza

This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…

Numerical Analysis · Mathematics 2014-12-01 Xiaobing Feng , Zhihao Ge , Yukun Li

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Richard S. Falk , Ragnar Winther

In this paper, we construct two lower order mixed elements for the linear elasticity problem in the Hellinger-Reissner formulation, one for the 2D problem and one for the 3D problem, both on macro-element meshes. The discrete stress spaces…

Numerical Analysis · Mathematics 2024-10-15 Jun Hu , Rui Ma , Yuanxun Sun

In this paper we introduce a mixed virtual element method to approximate the solution for the two dimensional generalized Oseen problem. We introduce the pseudostress as an additional unknown, which allows to eliminate the pressure from the…

Numerical Analysis · Mathematics 2026-01-29 Felipe Lepe , Gonzalo Rivera

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

In this work, we present and analyze a novel stabilized virtual element formulation for the coupled Stokes-Temperature equation on polygonal meshes, employing equal-order element pairs where viscosity depends on temperature. The main…

Numerical Analysis · Mathematics 2025-07-01 Sudheer Mishra , Natarajan E

We introduce and analyse a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a poroelastic medium.The flows in the free fluid and poroelastic regions are governed by the Navier-Stokes and…

Numerical Analysis · Mathematics 2025-12-16 Sergio Caucao , Aashi Dalal , 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 design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…

Numerical Analysis · Mathematics 2022-09-26 Franco Dassi , Alessio Fumagalli , Ilario Mazzieri , Giuseppe Vacca

This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve…

Numerical Analysis · Mathematics 2023-11-01 Zhibao Zheng , Udo Nackenhorst

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 develop and analyse an adaptive fully mixed finite element method for stationary generalized bioconvective flows, where the Navier--Stokes equations with concentration-dependent viscosity are coupled with a conservation law for swimming…

Numerical Analysis · Mathematics 2026-01-14 Eligio Colmenares , Ricardo Ruiz-Baier , Dalidet Sanhueza

A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarz\'ua and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer.…

Numerical Analysis · Mathematics 2019-12-13 Raimund Bürger , Sarvesh Kumar , David Mora , Ricardo Ruiz-Baier , Nitesh Verma

We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…

Numerical Analysis · Mathematics 2025-06-19 Soheil Firooz , B. Daya Reddy , Paul Steinmann

We develop a virtual element method to solve a convective Brinkman-Forchheimer problem coupled with a heat equation. This coupled model may allow for thermal diffusion and viscosity as a function of temperature. Under standard…

Numerical Analysis · Mathematics 2024-09-05 Danilo Amigo , Felipe Lepe , Enrique Otarola , Gonzalo Rivera

In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…

Numerical Analysis · Mathematics 2024-06-13 David Mora , Jesus Vellojin , Nitesh Verma

We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck equations, which are a nonlinear coupled system widely used in semiconductors and ion channels. The spatial…

Numerical Analysis · Mathematics 2022-07-18 Ying Yang , Ya Liu , Shi Shu

We extend the hybridization procedure proposed in [Arnold, Brezzi, 1985, ESAIM: M2AN] to the Virtual Element Method for linear elasticity problems based on the Hellinger-Reissner principle. To illustrate such a technique, we focus on the 2D…

Numerical Analysis · Mathematics 2021-03-02 Franco Dassi , Carlo Lovadina , Michele Visinoni

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