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The Well-Posedness and Discontinuous Galerkin Approximation for the Non-Newtonian Stokes–Darcy–Forchheimer Coupling System

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Abstract

We study the non-Newtonian Stokes–Darcy–Forchheimer system modeling the free fluid coupled with the porous medium flow with shear/velocity-dependent viscosities. The unique existence is proved by using the theory of nonlinear monotone operator and a coupled inf-sup condition. Moreover, we apply the discontinuous Galerkin (DG) method with \(P^k/P^{k-1}\)-DG element for numerical discretization and obtain the well-posedness, stability, and error estimate. For both the continuous and the discrete problem, we explore the convergence of the Picard iteration (or called Kacǎnov method). The theoretical results are confirmed by the numerical examples.

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610051, China

    Jingyan Hu

  2. Institute of Fundamental and Frontier Sciences and School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 610051, China

    Guanyu Zhou

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Correspondence to Jingyan Hu.

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The research was partially supported by NSFC General Projects No. 12171071,and the Natural Science Foundation of Sichuan Province (No. 2023NSFSC0055). All data generated or analysed during this study are included in this published article.

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Hu, J., Zhou, G. The Well-Posedness and Discontinuous Galerkin Approximation for the Non-Newtonian Stokes–Darcy–Forchheimer Coupling System. J Sci Comput 97, 24 (2023). https://doi.org/10.1007/s10915-023-02344-w

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