There have been growing research interests in high-order discontinuous schemes over
recent years. With established theoretical basis and framework, more efforts have recently …

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 …

This book is an introduction to a family of discontinuous Galerkin (DG) methods applied to
some steady-state and time-dependent model problems. A special effort was made to have …

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

We describe a limiter for the discontinuous Galerkin method that retains as high an order as
possible, and does not automatically reduce to first order. The limiter is a generalization of …

A new approach to slope limiting for discontinuous Galerkin methods on arbitrary meshes is
introduced. A local Taylor basis is employed to express the approximate solution in terms of …

We consider in this work the discontinuous Galerkin discretization of the nonlinear shallow
water equations on unstructured triangulations. In the recent years, several improvements …

A discrete fracture model for the flow of compressible, multicomponent fluids in
homogeneous, heterogeneous, and fractured media is presented in single phase. In the …

In this work, we present a numerical procedure that combines the mixed finite-element
(MFE) and the discontinuous Galerkin (DG) methods. This numerical scheme is used to …

In a recent work, we introduced a numerical approach that combines the mixed-finite-
element (MFE) and the discontinuous Galerkin (DG) methods for compositional modeling in …