hp DG Finite Element Methods For Incompressible Two-Phase Flow Models in
Porous Media

Ms. Yekaterina Epshteyn
University of Pittsburgh

In this presentation we will consider different formulations of the
incompressible two-phase flow problems arising in porous media:
``phase-pressure, phase-saturation'' formulation and ``global
pressure, phase-saturation'' formulation. We will introduce implicit,
fully coupled $hp$-schemes based on discontinuous Galerkin methods to
solve numerically the two-phase flow problems. Numerical analysis
(existence of the discrete solution, convergence) of the introduced
schemes and numerical examples of homogeneous and heterogeneous media
on structured and unstructured meshes will be shown.