Related papers: Edge-averaged virtual element methods for convecti…
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…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…
In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
This paper proposes a virtual element method (VEM) combined with a second-order implicit-explicit scheme based on the scalar auxiliary variable (SAV) method for the incompressible magnetohydrodynamics (MHD) equations. We employ the BDF2…
In this paper we introduce a mixed virtual element method to approximate the solution for the two dimensional generalized Oseen problem. We introduce the pseudostress as an additional unknown, which allows to eliminate the pressure from the…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…
The sparse activation mechanism of mixture of experts (MoE) model empowers edge intelligence with enhanced training efficiency and reduced computational resource consumption. However, traditional token routing in distributed MoE training…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…
The nonconforming Morley-type virtual element method for the incompressible Navier-Stokes equations formulated in terms of the stream-function on simply connected polygonal domains (not necessarily convex) is designed. A rigorous analysis…
In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE)…
We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…
Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilization, a divergence-free nonconforming…
This paper provides a rigorous convergence rate and complexity analysis for a recently introduced framework, called PDE acceleration, for solving problems in the calculus of variations, and explores applications to obstacle problems. PDE…
Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single…
This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in…
Robust recommendation aims at capturing true preference of users from noisy data, for which there are two lines of methods have been proposed. One is based on noise injection, and the other is to adopt the generative model Variational…