English
Related papers

Related papers: Spurious pressure in Scott-Vogelius elements

200 papers

We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…

Numerical Analysis · Mathematics 2023-10-09 Julius Jeßberger , Alex Kaltenbach

We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…

Fluid Dynamics · Physics 2011-10-07 Abdelkader Hammouti , Anaël Lemaître

We propose and analyse an augmented mixed finite element method for the Navier--Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation…

Numerical Analysis · Mathematics 2023-06-27 Veronica Anaya , Ruben Caraballo , Ricardo Ruiz-Baier , Hector Torres

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

In the same way as the energy density associated with the tensor modes of the geometry modifies the evolution of the curvature perturbations, the scalar modes may also indirectly affect the cosmic backgrounds of relic gravitons by inducing…

High Energy Physics - Theory · Physics 2020-10-07 Massimo Giovannini

In this paper, we propose a finite element pair for incompressible Stokes problem. The pair uses a slightly enriched piecewise linear polynomial space for velocity and piecewise constant space for pressure, and is illustrated to be a…

Numerical Analysis · Mathematics 2021-08-25 Wenjia Liu , Shuo Zhang

In this paper, we first construct a nonconforming finite element pair for the incompressible Stokes problem on quadrilateral grids, and then construct a discrete Stokes complex associated with that finite element pair. The finite element…

Numerical Analysis · Mathematics 2013-10-18 Shuo Zhang

This paper will suggest a new finite element method to find a $P^4$-velocity and a $P^3$-pressure solving incompressible Stokes equations at low cost. The method solves first the decoupled equation for a $P^4$-velocity. Then, using the…

Numerical Analysis · Mathematics 2023-10-26 Chunjae Park

We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. Using the multiple-scale technique, we perform an analytical calculation which allows us to predict the dynamics of such particles;…

Fluid Dynamics · Physics 2013-01-25 G. Boffetta , M. Martins Afonso , A. Mazzino , M. Onorato , F. Santamaria

We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and serve as a model problem in the dynamics of material…

Numerical Analysis · Mathematics 2018-01-23 Maxim A. Olshanskii , Annalisa Quaini , Arnold Reusken , Vladimir Yushutin

This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…

Numerical Analysis · Mathematics 2023-04-06 Yuwen Li , Ludmil Zikatanov

In this paper we investigate the qualitative behaviour of the pressure function beneath an extreme Stokes wave over infinite depth. The presence of a stagnation point at the wave-crest of an extreme Stokes wave introduces a number of…

Analysis of PDEs · Mathematics 2016-03-23 Tony Lyons

A computationally efficient, low order finite element formulation is developed for modelling the Navier-Stokes-Cahn-Hilliard equations, which have been established as a promising phase field modelling approach for simulation of immiscible…

Computational Physics · Physics 2019-11-18 Aleksander Lovrić , Wulf G. Dettmer , Djordje Perić

We propose to analyse the discretization of the Stokes problem with nonconforming finite elements in light of the T-coercivity (cf. [1] for Helmholtz-like problems, see [2], [3] and [4] for the neutron diffusion equation). We propose…

Analysis of PDEs · Mathematics 2022-11-03 Erell Jamelot

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete…

Numerical Analysis · Mathematics 2023-10-16 Maxim A. Olshanskii , Arnold Reusken , Paul Schwering

We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…

Numerical Analysis · Mathematics 2024-12-20 Jay Gopalakrishnan , Philip L. Lederer , Joachim Schöberl

We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial…

Probability · Mathematics 2012-01-05 Yutaka Terasawa , Nobuo Yoshida

Stokes variational inequalities arise in the formulation of glaciological problems involving contact. We consider the problem of a two-dimensional marine ice sheet with a grounding line, although the analysis presented here is extendable to…

Numerical Analysis · Mathematics 2022-10-12 Gonzalo G. de Diego , Patrick E. Farrell , Ian J. Hewitt

We investigate experimentally the spatial distributions of heavy and neutrally buoyant particles of finite size in a fully turbulent flow. As their Stokes number (i.e. ratio of the particle viscous relaxation time to a typical flow time…

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