Some DG schemes for the Stokes-Darcy problem using P1/P1 element

Abstract

We propose two new DG schemes based on the penalty and Nitsche's methods respectively for the Stokes-Darcy problem, where we adopt the P1/P1 elements for both the Stokes and Darcy's velocity/pressure. The well-posedness and a-priori estimates for the discrete solutions are established. The convergence order is elucidated by the numerical experiments.