Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media

Abstract

Abstract This paper presents and analyzes a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. We use a first-order time extrapolation, which allows us to solve the equations implicitly and sequentially. We show that the discrete problem is well posed, and obtain a priori error estimates. Our numerical results validate the theoretical results, i.e., the algorithm converges with first order.