In this paper, we review the development of the so-called local discontinuous Galerkin
method for linearized incompressible fluid flow. This is a stable, high-order accurate and …

In this paper, we develop the a posteriori error estimation of hp-version interior penalty
discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable …

We analyse the p-and hp-versions of the virtual element method (VEM) for the Stokes
problem on polygonal domains. The key tool in the analysis is the existence of a bijection …

Discontinuous Galerkin (DG) methods are a class of efficient tools for solving fluid flow
problems. There are in the literature many greatly successful DG methods. In this paper, a …

In this paper, we develop the a posteriori error estimation of mixed discontinuous Galerkin
finite element approximations of the Stokes problem. In particular, we derive computable …

We develop the a posteriori error estimation of mixed hp-version discontinuous Galerkin
finite element methods for nearly incompressible elasticity problems in two space …

This paper is the second part in a series on a mass conserving, high order, mixed finite
element method for Stokes flow. In this part, we construct optimal hp-approximations for two …

In this paper, we introduced the notion of an R ν-generalized solution of the Oseen problem
in rotation form in two-dimensional polygonal domain with a reentrant corner at the …

In this paper, we present a staggered discontinuous Galerkin method for the approximation
of the incompressible Navier–Stokes equations. Our new method combines the advantages …

The goal of this paper is to establish exponential convergence of hp-version interior penalty
(IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of …