相关论文: Vem++, a c++ library to handle and play with the V…

A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…

Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…

We present numerical tests of the Virtual Element Method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order "polynomial" degree (up to $p=10$). Besides, we discuss possible reasons for which the…

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 explore the use of the Virtual Element Method concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the active flux approach \cite{AF1}, which combines the usage of…

One remarkable feature of virtual element methods (VEMs) is their great flexibility and robustness when used on almost arbitrary polytopal meshes. This very feature makes it widely used in both fitted and unfitted mesh methods. Despite…

In this paper we present a framework for the construction and implementation of general virtual element spaces based on projections built from constrained least squares problems. Building on the triples used for finite element spaces, we…

We present two a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators are reliable and efficient for the $h$-, $p$-, and…

This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance…

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…

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 Virtual Element Method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a Balancing Domain Decomposition…

Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely…

In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose $C^1$ conforming virtual element method (VEM) of arbitrary order,…

In this paper, an enhanced Virtual Element Method (VEM) formulation is proposed for plane elasticity. It is based on the improvement of the strain representation within the element, without altering the degree of the displacement…

We present the novel Reduced Basis Virtual Element Method (rbVEM) for solving the Laplace eigenvalue problem. This approach is based on the virtual element method and exploits the reduced basis technique to obtain an explicit representation…

Variational algorithms are a representative class of quantum computing workloads that combine quantum and classical computing. This paper presents an LLVM-based C++ compiler toolchain to efficiently execute variational hybrid…