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 …

We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE)
methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground …

In this article we propose a new symmetric version of the interior penalty discontinuous
Galerkin finite element method for the numerical approximation of the compressible Navier …

In this paper we introduce the hp-version discontinuous Galerkin composite finite element
method for the discretization of second-order elliptic partial differential equations. This class …

An adaptive grid refinement method is presented for hydrodynamic flow simulation. It is
meant for application to a wide range of realistic flow problems, so generality and flexibility …

In this article we address the question of efficiently solving the algebraic linear system of
equations arising from the discretization of a symmetric, elliptic boundary value problem …

In this paper we present a 3-D dispersion and dissipation analysis for both the semi-discrete
and the fully discrete approximation of the elastodynamics equation based on the plane …

We develop duality-based a posteriori error estimates for functional outputs of solutions of
steady fluid–structure-interaction problems. The crucial complication in obtaining these …

We consider the adjoint-based error estimation and goal-oriented mesh refinement for
single and multiple aerodynamic force coefficients as well as residual-based mesh …

We consider semi-discrete discontinuous Galerkin approximations of both displacement and
displacement-stress formulations of the elastodynamics problem. We prove the stability …