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초록· 키워드
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A two-level finite element method based on the Newton iterative method is proposed for solving the Navier--Stokes/Darcy model. The algorithm solves a nonlinear system on a coarse mesh $H$ and two linearized problems of different loads on a fine mesh $h=O(H^{4-\epsilon})$. Compared with the common two-grid finite element methods for the considered problem, the presented two-level method allows for larger scaling between the coarse and fine meshes. Moreover, we prove the stability and convergence of the considered two-level method. Finally, we provide numerical experiment to exhibit the effectiveness of the presented method.
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참고문헌 (34)
참고문헌 신청
L. Badea / 2010 / Numerical analysis of the Navier-Stokes/Darcy coupling / Numer. Math 115(2):195~227
G. Beavers / 1967 / Boundary conditions at a naturally permeable wall / J. Fluid. Mech 30:197~207
Akram Boukabache / 2019 / A unified stabilized finite volume method for Stokes and Darcy equations / 대한수학회지 56(4):1083~1112
M. Cai / 2009 / Numerical solution to a mixed Navier-Stokes/Darcy model by the two-grid approach / SIAM J. Numer. Anal 47(5):3325~3338
Y. Cao / 2013 / Decoupling the stationary Navier-Stokes-Darcy system with the Beavers-Joseph-Saman interface condition / Abstr. Appl. Anal 2013:10
G. Beavers / 1967 / Boundary conditions at a naturally permeable wall / J. Fluid. Mech 30:197~207
Akram Boukabache / 2019 / A unified stabilized finite volume method for Stokes and Darcy equations / 대한수학회지 56(4):1083~1112
M. Cai / 2009 / Numerical solution to a mixed Navier-Stokes/Darcy model by the two-grid approach / SIAM J. Numer. Anal 47(5):3325~3338
Y. Cao / 2013 / Decoupling the stationary Navier-Stokes-Darcy system with the Beavers-Joseph-Saman interface condition / Abstr. Appl. Anal 2013:10
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