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In two and three dimensional domains, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The methods consist in two schemes: the velocity and pressure are approximated…

Numerical Analysis · Mathematics 2021-03-09 Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

We introduce two new lowest order methods, a mixed method, and a hybrid Discontinuous Galerkin (HDG) method, for the approximation of incompressible flows. Both methods use divergence-conforming linear Brezzi-Douglas-Marini space for…

Numerical Analysis · Mathematics 2023-04-04 Jay Gopalakrishnan , Lukas Kogler , Philip L. Lederer , Joachim Schöberl

This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…

Numerical Analysis · Mathematics 2019-04-01 Eric Chung , Yalchin Efendiev , Wing Tat Leung

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

This paper presents the numerical solution of immiscible two-phase flows in porous media, obtained by a first-order finite element method equipped with mass-lumping and flux up-winding. The unknowns are the physical phase pressure and phase…

Numerical Analysis · Mathematics 2021-11-24 M. S. Joshaghani , V. Girault , B. Riviere

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

In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…

We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane…

General Mathematics · Mathematics 2023-05-30 Aymen Laadhari , Ahmad Deeb

In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been first introduced for the…

Numerical Analysis · Mathematics 2014-01-06 Sébastien Court , Michel Fournié , Alexei Lozinski

In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…

Numerical Analysis · Mathematics 2021-01-19 Xiaoxiao He , Fei Song , Weibing Deng

We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…

Numerical Analysis · Mathematics 2015-06-02 John W. Barrett , Harald Garcke , Robert Nürnberg

A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…

Fluid Dynamics · Physics 2014-08-11 Jun-De Li

In this paper, two approaches for modeling three-component fluid flows using diffusive interface method are discussed. Thermodynamic consistency of the proposed models is preserved when using an energetic variational framework to derive the…

Analysis of PDEs · Mathematics 2018-10-12 Arkadz Kirshtein , James Brannick , Chun Liu

We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present…

Soft Condensed Matter · Physics 2016-08-31 Keir E. Novik , Peter V. Coveney

This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and…

Numerical Analysis · Mathematics 2024-05-21 Tom Gustafsson , Juha Videman

We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…

Numerical Analysis · Mathematics 2020-05-05 Gabriel N. Gatica , Antonio Márquez , Salim Meddahi

Quantifying the contribution of vortex structures to pressure stress is useful for designing flow control strategies to mitigate low or drag. The traditional force-element method focuses on the contribution of vortex structures to the…

Fluid Dynamics · Physics 2025-09-16 Zhiteng Zhou , Yi Liu , Hongping Wang , Shizhao Wang

Divergence-free discontinuous Galerkin (DG) finite element methods offer a suitable discretization for the pointwise divergence-free numerical solution of Borrvall and Petersson's model for the topology optimization of fluids in Stokes flow…

Numerical Analysis · Mathematics 2022-02-22 Ioannis P. A. Papadopoulos

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…

Numerical Analysis · Mathematics 2018-10-22 Christoph Erath , Günther Of , Francisco-Javier Sayas

In this work, a new discretization approach for coupled free and porous-medium flows is introduced, which uses a finite volume staggered-grid method for the discretization of the Navier-Stokes equations in the free-flow subdomain, while a…

Numerical Analysis · Mathematics 2021-12-22 Martin Schneider , Dennis Gläser , Kilian Weishaupt , Edward Coltman , Bernd Flemisch , Rainer Helmig