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

## TL;DR

This paper presents an embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system, achieving optimal convergence and divergence-conforming velocities, verified through numerical experiments.

## Contribution

The paper introduces a novel EDG-HDG discretization that ensures mass conservation and divergence conformity for coupled Stokes-Darcy problems.

## Key findings

- Achieves optimal convergence rates.
- Velocity error independent of pressure.
- Validated on unstructured grids with various polynomial orders.

## Abstract

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.