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In this paper we analyze a virtual element method (VEM) for a pseudostress formulation of the Stokes eigenvalue problem. This formulation allows to eliminate the velocity and the pressure, leading to an elliptic formulation where the only…

Numerical Analysis · Mathematics 2021-04-07 Felipe Lepe , Gonzalo Rivera

This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…

Fluid Dynamics · Physics 2025-09-24 Alessandro Aiello , Carlo De Michele , Gennaro Coppola

In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the…

Numerical Analysis · Mathematics 2023-01-16 Remi Abgrall , Paola Bacigaluppi , Tokareva Svetlana

We construct and analyze first- and second-order implicit-explicit (IMEX) schemes based on the scalar auxiliary variable (SAV) approach for the magneto-hydrodynamic equations. These schemes are linear, only require solving a sequence of…

Numerical Analysis · Mathematics 2021-04-02 Xiaoli Li , Weilong Wang , Jie Shen

We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…

Numerical Analysis · Mathematics 2025-09-24 Aaron Baier-Reinio , Patrick E. Farrell

A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…

Computational Physics · Physics 2018-05-25 Xiaoyu Feng , Jisheng Kou , Shuyu Sun

In this paper, we discuss a virtual element approximation for the modified transmission eigenvalue problem in inverse scattering for natural materials. In this case, due to the positive artificial diffusivity parameter in the considered…

Numerical Analysis · Mathematics 2025-10-30 Liangkun Xu , Shixi Wang , Hai Bi

This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…

Numerical Analysis · Mathematics 2021-08-11 Flávio Luiz Cardoso-Ribeiro , Denis Matignon , Laurent Lefèvre

Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…

Numerical Analysis · Mathematics 2025-06-13 Igor Tominec , Lukas Lundgren , André Löfgren , Josefin Ahlkrona

In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the…

Numerical Analysis · Mathematics 2016-01-20 Arvind Baskaran , Zhen Guan , John Lowengrub

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 introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…

Numerical Analysis · Mathematics 2026-04-16 Paola F. Antonietti , Francesca Bonizzoni , Ilaria Perugia , Marco Verani

We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [59] the problem is supposed to have a unique solution, but…

Numerical Analysis · Mathematics 2014-12-09 L. Beirão da Veiga , F. Brezzi , L. D. Marini , A. Russo

In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an initial value problem (IVP) for the partial differential…

Numerical Analysis · Mathematics 2022-07-18 Siting Liu , Stanley Osher , Wuchen Li , Chi-Wang Shu

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…

Numerical Analysis · Mathematics 2018-02-09 Francesca Gardini , Gianmarco Manzini , Giuseppe Vacca

Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonical Hamiltonian formulation with a number of conserved…

Computational Physics · Physics 2018-08-29 Michael Kraus

A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…

Numerical Analysis · Mathematics 2019-03-12 Buyang Li , Jilu Wang , Liwei Xu

The present work is devoted to introduce the backward Euler based modular time filter method for MHD flow. The proposed method improves the accuracy of the solution without a significant change in the complexity of the system. Since time…

Numerical Analysis · Mathematics 2019-06-20 Aytekin Cibik , Fatma G. Eroglu , Songul Kaya

We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed…

Numerical Analysis · Mathematics 2024-02-08 Jinpeng Zhang , Changjuan Zhang , Xiaoping Wang

We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…

Numerical Analysis · Mathematics 2019-02-20 Huadong Gao , Weifeng Qiu