In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an
attractive approach for numerical simulations of compressible flows. This paper presents an …

This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

Theoretical studies and numerical experiments suggest that unstructured high-order
methods can provide solutions to otherwise intractable fluid flow problems within complex …

In the present paper we introduce a Virtual Element Method (VEM) for the approximate
solution of general linear second order elliptic problems in mixed form, allowing for variable …

We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes
having test function spaces that are automatically computable to guarantee stability. Given a …

In this paper we present an efficient discretization method for the solution of the unsteady
incompressible Navier–Stokes equations based on a high order (Hybrid) Discontinuous …

We present an implicit high-order hybridizable discontinuous Galerkin method for the steady-
state and time-dependent incompressible Navier–Stokes equations. The method is devised …

Considering a simple model transport problem, we present a new finite element method.
While the new method fits in the class of discontinuous Galerkin (DG) methods, it differs from …

In this paper, we introduce a hybridizable discontinuous Galerkin method for Stokes flow.
The method is devised by using the discontinuous Galerkin methodology to discretize a …

In this paper, we review and refine the main ideas for devising the so-called hybridizable
discontinuous Galerkin (HDG) methods; we do that in the framework of steady-state diffusion …