相关论文: A Nonconforming Virtual Element Method for Advecti…
For the stationary advection-diffusion problem the standard continuous Galerkin method is unstable without some additional control on the mesh or method. The interior penalty discontinuous Galerkin method is stable but at the expense of an…
This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties…
For the solution of 2D exterior Dirichlet Poisson problems we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error…
In the present paper we initiate the challenging task of building a mathematically sound theory for Adaptive Virtual Element Methods (AVEMs). Among the realm of polygonal meshes, we restrict our analysis to triangular meshes with hanging…
There is a wide range of stabilized finite element methods for stationary and non-stationary convection-diffusion equations such as streamline diffusion methods, local projection schemes, subgrid-scale techniques, and continuous interior…
Low-order virtual element methods (VEM) compute a consistent finite-strain contribution through polynomial projections and rely on stabilization to control the unresolved modes in the projector kernel. In current hyperelastic VEM practice,…
In this work, we review the framework of the Virtual Element Method (VEM) for a model in magneto-hydrodynamics (MHD), that incorporates a coupling between electromagnetics and fluid flow, and allows us to construct novel discretizations for…
The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity…
In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…
The Morley finite element method (FEM) is attractive for semilinear problems with the biharmonic operator as a leading term in the stream function vorticity formulation of 2D Navier-Stokes problem and in the von K\'{a}rm\'{a}n equations.…
The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with…
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
In this paper, we employ the linear virtual element spaces to discretize the semilinear sine-Gordon equation in two dimensions. The salient features of the virtual element method (VEM) are: (a) it does not require explicit form of the shape…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…
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…
The third medium contact has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, the third medium contact introduces a third medium between two…