A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes and Darcy problem

TL;DR

This paper introduces a hybridizable discontinuous Galerkin method for solving coupled Navier-Stokes and Darcy equations, ensuring velocity accuracy independent of pressure and achieving optimal convergence rates, validated through numerical tests.

Contribution

The paper develops a strongly conservative hybridizable discontinuous Galerkin method for coupled Navier-Stokes and Darcy problems with proven optimal error estimates.

Findings

Velocity error is independent of pressure.

Velocity and pressure converge at optimal rates.

Numerical examples confirm theoretical results.

Abstract

We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers-Joseph-Saffman interface condition. An a priori error analysis shows that the velocity error does not depend on the pressure, and that velocity and pressure converge with optimal rates. These results are confirmed by numerical examples.