An embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system

We introduce an embedded-hybridized discontinuous Galerkin (EDG-HDG) method for the coupled Stokes-Darcy system. This EDG-HDG method is a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the whole domain. In the proposed scheme, coupling between the Stokes and Darcy domains is achieved naturally through the EDG-HDG facet variables. \emph{A priori} error analysis shows optimal convergence rates, and that the velocity error does not depend on the pressure. The error analysis is verified through numerical examples on unstructured grids for different orders of polynomial approximation

Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media

We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous finite volume element methods in combination with the optimise-then-discretise approach for the approximation of the optimal control problem, leading to nonsymmetric algebraic systems, and employing minimum regularity requirements. Estimates for the error (between a local reference solution of the infinite dimensional optimal control problem and its hybrid approximation) measured in suitable norms are derived, showing optimal orders of convergence