We present, in a unified framework, new conforming and nonconforming virtual element
methods for general second-order elliptic problems in two and three dimensions. The …

Poincaré--Friedrichs Inequalities for Piecewise H1 Functions Page 1 POINCARÉ–FRIEDRICHS
INEQUALITIES FOR PIECEWISE H1 FUNCTIONS∗ SUSANNE C. BRENNER† SIAM J …

We present the nonconforming virtual element method (VEM) for the numerical
approximation of velocity and pressure in the steady Stokes problem. The pressure is …

It is well-known that on uniform meshes the piecewise linear conforming finite element
solution of the Poisson equation approximates the interpolant to a higher order than the …

AP 1-nonconforming quadrilateral finite element is introduced for second-order elliptic
problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements …

In this paper a unified nonconforming virtual element scheme for the Navier-Stokes
equations with different dimensions and different polynomial degrees is described. Its key …

Since the nonconforming P1 finite element method for the Stokes equations was introduced
by M. Crouzeix and PA Raviart in 1973, there have been many advances in the finite …

Residual-based a posteriori error estimates were derived within one unifying framework for
lowest-order conforming, nonconforming, and mixed finite element schemes in Carstensen …

In this article, we develop and analyze a mixed finite element method for the Stokes
equations. Our mixed method is based on the pseudostress‐velocity formulation. The …

The main aim of this paper is to study the error estimates of a rectangular nonconforming
finite element for the stationary Navier–Stokes equations under anisotropic meshes. That is …