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

被引:0
作者
Araya, Rodolfo [1 ,2 ]
Carcamo, Cristian [5 ]
Poza, Abner H. [3 ,4 ]
Vino, Eduardo [3 ]
机构
[1] Univ Concepcion, Dept Ingn Matemat, Casilla 160-C, Concepcion, Chile
[2] Univ Concepcion, CI MA 2, Casilla 160-C, Concepcion, Chile
[3] Univ Catolica Santisima Concepcion, Dept Matemat & Fis Aplicadas, Casilla 297, Concepcion, Chile
[4] Grp Invest Anal Numer & Calculo Cientif, GIANuC 2, Concepcion, Chile
[5] Leibniz Inst Forsch Verbund Berlin EV WIAS, Weierstrass Inst Angew Anal & Stochast, Berlin, Germany
关键词
Coupled Stokes-Darcy equation; Stabilized finite element method; A priori error analysis; A posteriori error analysis; FLUID-FLOW; BOUNDARY-CONDITIONS; FORMULATIONS;
D O I
10.1016/j.cam.2024.115753
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页数:24
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