A control volume finite element approach to NAPL groundwater contamination
SIAM Journal on Scientific and Statistical Computing
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Fundamentals of Numerical Reservoir Simulation
Fundamentals of Numerical Reservoir Simulation
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
A Finite Volume Scheme for Two-Phase Immiscible Flow in Porous Media
SIAM Journal on Numerical Analysis
Discontinuous galerkin finite element methods applied to two-phase, air-water flow problems
Discontinuous galerkin finite element methods applied to two-phase, air-water flow problems
Journal of Computational Physics
Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow
Journal of Computational and Applied Mathematics
On the coupling of finite volume and discontinuous Galerkin method for elliptic problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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In this paper we present two schemes based on discontinuous Galerkin methods for modeling fully implicit formulations of two-phase flow problems arising in porous media. Convergence with respect to uniform mesh refinement or increase in the polynomial degree are considered. Compared to sequential discontinuous schemes, our proposed schemes do not require slope limiting or upwind stabilization techniques. Numerical examples of homogeneous and heterogeneous media on structured and unstructured meshes show the robustness of the method.