相关论文: FETI-DP preconditioners for the Virtual Element Me…

In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains with inexact subdomain solvers. Recently, the authors have…

The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…

We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a model…

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to…

Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…

A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…

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…

The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…

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…

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…

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 Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the…

In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…

In this paper, we develop the auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the second order elliptic equations. The preconditioners are…

Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…

This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…

This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…

We establish a simple, rigorous, and easy to implement connection between the classical continuous finite element method (FEM) and the discontinuous Galerkin (DG) method for Poisson's problem. The key idea is to insert a vanishing-thickness…

This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…