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 …

Emerging as the mathematical expression of principles of conservation, conservation laws
have proven themselves to provide effective and accurate predictive models of our physical …

Abstract Hybrid High-Order (HHO) methods are formulated in terms of discrete unknowns
attached to mesh faces and cells (hence, the term hybrid), and these unknowns are …

We propose and analyse a symmetric weighted interior penalty method to approximate in a
discontinuous Galerkin framework advection–diffusion equations with anisotropic and …

Two discrete functional analysis tools are established for spaces of piecewise polynomial
functions on general meshes:(i) a discrete counterpart of the continuous Sobolev …

A continuous interior penalty $ hp $-finite element method that penalizes the jump of the
gradient of the discrete solution across mesh interfaces is introduced. Error estimates are …

We apply the weighted-residual approach recently introduced in [F. Brezzi et al., Comput.
Methods Appl. Mech. Engrg., 195 (2006), pp. 3293–3310] to derive discontinuous Galerkin …

Water and air behave in a similar way and their flow can be described in a very accurate
way by the Navier–Stokes equations. Others fluids behave differently: they cannot be …

This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

In this paper, we present some improvements, in terms of accuracy and speed-up, for a
particular well adapted Discontinuous Galerkin method devoted to the time-domain Maxwell …