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We will present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. The wellposedness of this PDE model is established by means of constructing for it a…

Analysis of PDEs · Mathematics 2014-02-26 George Avalos , Thomas J. Clark

We propose first-order pressure-correction scheme for the incompressible Navier-Stokes equations, incorporating the recently developed the Dynamically Regularized Lagrange Multiplier (DRLM) methods. The resulting algorithms are fully…

Numerical Analysis · Mathematics 2026-03-18 Yi Shen , Rihui Lan , Hua Wang

A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the…

Numerical Analysis · Mathematics 2017-03-07 L. Beirão da Veiga , C. Lovadina , G. Vacca

This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…

Numerical Analysis · Mathematics 2024-05-13 Sarvesh Kumar , Devika Shylaja

In this paper we propose a new high order accurate space-time DG finite element scheme for the solution of the linear elastic wave equations in first order velocity-stress formulation in two and three-space dimensions on staggered…

Numerical Analysis · Mathematics 2018-05-09 Maurizio Tavelli , Michael Dumbser

The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic…

Numerical Analysis · Mathematics 2018-10-24 Edoardo Artioli , Lourenco Beirão da Veiga , Carlo Lovadina , Elio Sacco

In this paper, we propose a new approach for the time-discretization of the incompressible stochastic Stokes equations with multiplicative noise. Our new strategy is based on the classical Milstein method from stochastic differential…

Numerical Analysis · Mathematics 2022-12-08 Liet Vo

Discretization of Navier-Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in…

Numerical Analysis · Mathematics 2020-07-09 Naveed Ahmed , Gabriel R. Barrenechea , Erik Burman , Johnny Guzmán , Alexander Linke , Christian Merdon

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

This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…

Numerical Analysis · Mathematics 2026-02-04 Paola F. Antonietti , Alessandra Cancrini , Gabriele Ciaramella

This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the…

Numerical Analysis · Mathematics 2024-12-02 Yu Xiong , Yanping Chen

We investigate artificial compressibility (AC) techniques for the time discretization of the incompressible Navier-Stokes equations. The space discretization is based on a lowest-order face-based scheme supporting polytopal meshes, namely…

Numerical Analysis · Mathematics 2021-05-04 Riccardo Milani , Jérôme Bonelle , Alexandre Ern

A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…

Numerical Analysis · Mathematics 2014-11-27 F. Guillén-González , M. V. Redondo-Neble

For the 2D and 3D Virtual Element Methods (VEM), a new approach to improve the conditioning of local and global matrices in the presence of badly-shaped polytopes is proposed. It defines the local projectors and the local degrees of freedom…

Numerical Analysis · Mathematics 2023-12-01 Stefano Berrone , Gioana Teora , Fabio Vicini

This work presents a novel reduced-order model (ROM) for the incompressible Navier-Stokes equations with time-dependent boundary conditions. This ROM is velocity-only, i.e. the simulation of the velocity does not require the computation of…

Numerical Analysis · Mathematics 2022-12-26 Henrik Rosenberger , Benjamin Sanderse

The aim of this paper is to analyze a mixed formulation for the two dimensional Stokes eigenvalue problem where the unknowns are the stress and the velocity, whereas the pressure can be recovered with a simple postprocess of the stress. The…

Numerical Analysis · Mathematics 2022-03-03 Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

We develop $H$(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is…

Numerical Analysis · Mathematics 2024-10-21 Costanza Aricò , Rainer Helmig , Ivan Yotov

We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is…

Numerical Analysis · Mathematics 2019-02-12 Christian Kreuzer , Pietro Zanotti

In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood…

Numerical Analysis · Mathematics 2025-12-03 Charles M. Elliott , Achilleas Mavrakis

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…

Mathematical Software · Computer Science 2015-06-04 J. A. F. Hittinger , J. W. Banks