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We present a novel stabilized isogeometric formulation for the Stokes problem, where the geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) patches, i.e., one patch on top of another in an arbitrary but…

Numerical Analysis · Mathematics 2023-09-22 Xiaodong Wei , Riccardo Puppi , Pablo Antolin , Annalisa Buffa

In this paper we analyze a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. We consider the classic velocity-pressure formulation which allows us to…

Numerical Analysis · Mathematics 2024-05-24 Danilo Amigo , Felipe Lepe , Nitesh Verma

We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case…

Numerical Analysis · Mathematics 2024-08-02 Silvia Bertoluzza , Monica Montardini , Micol Pennacchio , Daniele Prada

We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to…

Numerical Analysis · Mathematics 2025-11-17 Katharina Kormann , Murtazo Nazarov , Junjie Wen

We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the velocity. The…

Numerical Analysis · Mathematics 2021-11-04 Veronica Anaya , Ruben Caraballo , Bryan Gomez-Vargas , David Mora , Ricardo Ruiz-Baier

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…

Numerical Analysis · Mathematics 2015-06-15 Sébastien Court , Michel Fournié , Alexei Lozinski

We develop a Nitsche fictitious domain method for the Stokes problem starting from a stabilized Galerkin finite element method with low order elements for both the velocity and the pressure. By introducing additional penalty terms for the…

Numerical Analysis · Mathematics 2012-06-12 Andre Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…

Numerical Analysis · Mathematics 2024-09-23 Evan S. Gawlik , François Gay-Balmaz

Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the…

Numerical Analysis · Mathematics 2024-10-21 Patrick Ciarlet , Erell Jamelot

In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…

Numerical Analysis · Mathematics 2013-08-05 Erik Burman

We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations.…

Numerical Analysis · Mathematics 2022-12-21 Alvin Chen , N. Sukumar

We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and…

Numerical Analysis · Mathematics 2023-06-07 Sarvesh Kumar , David Mora , Ricardo Ruiz-Baier , Nitesh Verma

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

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 introduce a new finite element method for solving the Stokes equations in the primary velocity-pressure formulation. This method employs $H(div)$ finite elements to approximate velocity, which leads to two unique…

Numerical Analysis · Mathematics 2020-06-23 Xiu Ye , Shangyou Zhang

A stationary Stokes problem with a piecewise constant viscosity coefficient in multiple subdomains is considered in the paper. For standard finite element pairs, a robust inf-sup condition is required to show the robustness of the…

Numerical Analysis · Mathematics 2025-07-22 Yuxiang Liang , Shun Zhang

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the…

Numerical Analysis · Mathematics 2017-07-06 Jean-Claude Latché , Khaled Saleh

In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and…

Numerical Analysis · Mathematics 2026-04-07 Liangkun Xu , Shixi Wang , Yidu Yang , Hai Bi

We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…

Numerical Analysis · Mathematics 2015-07-22 Arun L. Gain , Cameron Talischi , Glaucio H. Paulino

We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…

Numerical Analysis · Mathematics 2018-07-24 Erik Burman , Peter Hansbo , Mats G. Larson , Andre Massing , Sara Zahedi