A refined a priori error analysis of the lowest order (linear) virtual element method (VEM) is
developed for approximating a model two-dimensional Poisson problem. A set of new …

We prove the optimal convergence estimate for first-order interpolants used in finite element
methods based on three major approaches for generalizing barycentric interpolation …

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear
element under quadrilateral meshes. It has been proven that the recovered gradient …

Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and
Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity …

In this paper, we analyze a stabilized equal‐order finite element approximation for the
Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a …

Interpolation operators map a function u to an element I u of a finite element space. Unlike
more general approximation operators, interpolants are defined locally. Estimates of the …

An average interpolation is introduced for 3-rectangles and tetrahedra, and optimal order
error estimates in the H1 norm are proved. The constant in the estimate depends …

In this paper we use P 1-nonconforming quadrilateral finite volume methods with
interpolated coefficients to solve the semilinear elliptic problems. Two types of control …

Several quadrilateral shape regular mesh conditions commonly used in the finite element
method are proven to be equivalent. Their influence on the finite element interpolation error …

A new finite element method is proposed for second order elliptic interface problems based
on a local anisotropic fitting mixed mesh. The local anisotropic fitting mixed mesh is …