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 …

In this paper, we formulate and test numerically a fully-coupled discontinuous Galerkin (DG)
method for incompressible two-phase flow with discontinuous capillary pressure. The spatial …

We design and investigate a sequential discontinuous Galerkin method to approximate two-
phase immiscible incompressible flows in heterogeneous porous media with discontinuous …

In this paper, we propose an enriched Galerkin (EG) approximation for a two-phase
pressure saturation system with capillary pressure in heterogeneous porous media. The EG …

This paper develops a general abstract framework for a posteriori estimates for immiscible
incompressible two-phase flows in porous media. We measure the error by the dual norm of …

In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the
coupled system of compressible miscible displacement problems. We consider the problem …

We consider the slightly compressible two-phase flow problem in a porous medium with
capillary pressure. The problem is solved using the implicit pressure, explicit saturation …

In this paper, we develop high-order bound-preserving (BP) discontinuous Galerkin (DG)
methods for the coupled system of compressible miscible displacements on triangular …

We present a high-order method for miscible displacement simulation in porous media. The
method is based on discontinuous Galerkin discretization with weighted average …

The focus of the present work is to model the two-phase flow of oil and water in 2-D
anisotropic petroleum reservoirs using a novel appropriate combination of a non-orthodox …