相关论文: SUPG-stabilized stabilization-free VEM: a numerica…
In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…
We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) for the Poisson problem. The method allows the definition of bilinear forms that do not require a stabilization term, thanks to the exploitation…
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…
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,…
We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an $H^1(\Omega)$-conforming discretization by means of VEM which can make use of general polygonal…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
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…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
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 initiate the design and the analysis of stabilization-free Virtual Element Methods for the laplacian problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the…
This paper presents the development and analysis of a streamline upwind/Petrov-Galerkin (SUPG) method for the magnetic advection-diffusion problem. A key feature of the method is an SUPG-type stabilization term based on the residuals and…
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…
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
The Adaptive Stabilized Finite Element method (AS-FEM) developed in Calo et. al. combines the idea of the residual minimization method with the inf-sup stability offered by the discontinuous Galerkin (dG) frameworks. As a result, 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…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
In this paper, we analyze a virtual element method (VEM) for solving a non-selfadjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. We write a variational formulation and propose a $C^1$-conforming…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These…