Geodesic
Finite element method for the Stokes–Darcy problem with a new boundary condition
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 2, pp. 165-181

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This paper considers numerical methods for approaching and simulate the Stokes–Darcy problem, with a new boundary condition. We study herein a robust stabilized fully mixed discretization technique, this method ensures the stability of the finite element scheme and does not use any Lagrange multipliers to introduce a stabilization term in the temporal Stokes–Darcy problem discretization. The well-posedness of the finite element scheme and its convergence analysis are also derived. Finally, the efficiency and accuracy of the numerical methods are illustrated by different numerical tests 
@article{SJVM_2020_23_2_a5,
     author = {O. El Moutea and H. El Amri and A. El Akkad},
     title = {Finite element method for the {Stokes{\textendash}Darcy} problem with a new boundary condition},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {165--181},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2020_23_2_a5/}
}
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O. El Moutea; H. El Amri; A. El Akkad. Finite element method for the Stokes–Darcy problem with a new boundary condition. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 2, pp. 165-181. http://geodesic.mathdoc.fr/item/SJVM_2020_23_2_a5/