Approximations by mini mixed finite element for the Stokes-Darcy coupled problem on curved domains

Abstract

In this work we solve a Stokes-Darcy coupled problem in a plane curved domain using curved elements. We approximate the velocity-pressure pair by applying the MINI-element method, for the whole coupled problem. We show that, under appropriate assumptions about the curved domain, the proposed method has optimal accuracy, with respect to solution regularity, and has a simple implementation. We also present numerical tests which show the good performance of the proposed method.