相关论文: A first-order stabilization-free Virtual Element M…

The present paper has two objectives. On one side, we develop and test numerically divergence free Virtual Elements in three dimensions, for variable ``polynomial'' order. These are the natural extension of the two-dimensional divergence…

A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…

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…

In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of…

In this paper, we develop a robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs), superiorly handling the cases of small or vanishing lower bound of the VO function. The valid fast…

In this paper we analyze a lowest order virtual element method for the load classic reaction-convection-diffusion problem and the convection-diffusion spectral problem, where the assumptions on the polygonal meshes allow to consider small…

We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic…

In this paper we propose and analyze a virtual element method for the two dimensional non-symmetric diffusion-convection eigenvalue problem in order to derive a priori and a posteriori error estimates. Under the classic assumptions of the…

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. We adopt the Hellinger--Reissner variational principle to construct a weak equilibrium…

In this work, we investigate Vacuum-Packed Particle (VPP) dampers -- granular-core dampers offering tunable damping performance -- as a more sustainable alternative to conventional systems such as magnetorheological fluid dampers. A…

There is a wide range of stabilized finite element methods for stationary and non-stationary convection-diffusion equations such as streamline diffusion methods, local projection schemes, subgrid-scale techniques, and continuous interior…

The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the resulting linear systems are often ill-conditioned and…

Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…

This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…

In this work, we develop recent research on the fully mixed virtual element method (mixed-VEM) based on the Banach space for the stationary Boussinesq equation to suggest and analyze a new mixed-VEM for the stationary two-dimensional…

The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain is analyzed under reduced elliptic regularity. The…

This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equations that support arbitrary orders and polyhedral meshes.…

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…

A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved…