Related papers: Sharper error estimates for Virtual Elements and a…
We study the $h$- and $p$-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use…
We introduce non conforming virtual elements to approximate the eigenvalues and eigenfunctions of the two dimensional acoustic vibration problem. We focus our attention on the pressure formulation of the acoustic vibration problem in order…
In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
Finite element methods are well-known to admit robust optimal convergence on simplicial meshes satisfying the maximum angle conditions. But how to generalize this condition to polyhedra is unknown in the literature. In this work, we argue…
In this paper, we prove a discrete embedding inequality for the Raviart--Thomas mixed finite element methods for second order elliptic equations, which is analogous to the Sobolev embedding inequality in the continuous setting. Then, by…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final…
We develop a class of mixed virtual volume methods for elliptic problems on polygonal/polyhedral grids. Unlike the mixed virtual element methods introduced in \cite{brezzi2014basic,da2016mixed}, our methods are reduced to symmetric,…
The lowest-order Neural Approximated Virtual Element Method on polygonal elements is proposed here. This method employs a neural network to locally approximate the Virtual Element basis functions, thereby eliminating issues concerning…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes…
In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E$^2$VEM) with the focus on some elliptic test problems whose solution and diffusivity…
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal…
We construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have…
In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly-anisotropic diffusion problems. In particular, we analyze the performances of different approaches which are…
The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that…