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A two-level finite element method for the steady-state Navier--Stokes/Darcy model

Yi Qin|Jilin Fang|Pengzhan Huang
대한수학회 (The Korean Mathematical Society)|2020.07|대한수학회지 (Journal of the KMS)|제57권 제4호|pp. 915-933|DOI 10.4134/JKMS.j190449

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키워드

scalinginterface conditionsNewton iterationNavier--Stokes/Darcy modeltwo-level method
주제분류수학

초록

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.

Abstract

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.

참고문헌 (34)

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