An adaptive stabilized finite element method for the Stokes-Darcy coupled problem

Araya, Rodolfo; Carcamo, Cristian; Poza, Abner H.; Vino, Eduardo

Abstract

For the Stokes-Darcy coupled problem, which models a fluid that flows from a free medium into a porous medium, we introduce and analyze an adaptive stabilized finite element method using Lagrange equal order element to approximate the velocity and pressure of the fluid. The interface conditions between the free medium and the porous medium are given by mass conservation, the balance of normal forces, and the Beavers-Joseph-Saffman conditions. We prove the well-posedness of the discrete problem and present a convergence analysis with optimal error estimates in natural norms. Next, we introduce and analyze a residual -based a posteriori error estimator for the stabilized scheme. Finally, we present numerical examples to demonstrate the performance and effectiveness of our scheme.

Más información

Título según WOS: ID WOS:001167900000001 Not found in local WOS DB
Título de la Revista: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volumen: 443
Editorial: Elsevier
Fecha de publicación: 2024
DOI:

10.1016/j.cam.2024.115753

Notas: ISI