相关论文: An adaptive virtual element method for the polymer…

We introduce a novel residual-based a posteriori error estimator for the conforming $C^1$ Virtual Element Method (VEM) applied to the buckling eigenvalue problem, incorporating nonlinear plane stress effects in both two and three…

The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…

We present a priori and a posteriori error analysis of a Virtual Element Method (VEM) to approximate the vibration frequencies and modes of an elastic solid. We analyze a variational formulation relying only on the solid displacement and…

This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…

Since its introduction, the Virtual Element Method (VEM) was shown to be able to deal with a large variety of polygons, while achieving good convergence rates. The regularity assumptions proposed in the VEM literature to guarantee the…

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…

In this work, we explore the application of Stabilization-Free Virtual Element Methods for Neumann boundary Optimal Control Problems in saddle point formulation. The method is proposed for arbitrary polynomial order of accuracy and general…

This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…

We introduce a novel virtual element method (VEM) for the two dimensional Helmholtz problem endowed with impedance boundary conditions. Local approximation spaces consist of Trefftz functions, i.e., functions belonging to the kernel of the…

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…

We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed…

We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFEM modifies the classical adaptive finite element method…

This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…

We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving moving boundaries. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary…

We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…

This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order Virtual Element Method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both…

The focus of this study is the construction and numerical validation of parallel block preconditioners for low order virtual element discretizations of the three-dimensional Maxwell equations. The virtual element method (VEM) is a recent…

In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning…

In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…