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Two-grid method for compressible miscible displacement problem by mixed finite element methods and expanded mixed finite element method of characteristics

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Abstract

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium by employing a mixed finite element method (MFEM) for the pressure equation and expanded mixed finite element method with characteristics (CEMFEM) for the concentration equation. The key point is to use a two-grid scheme to linearize the nonlinear term in the coupling equations. The main procedure of the algorithm is to solve small scaled nonlinear equations on the coarse grid and to deal with a linearized system on the fine space using the Newton iteration with the coarse grid solution. Then, it is shown that a two-grid algorithm achieves optimal approximation as long as the mesh sizes satisfy \(H = O(h^{\frac {1}{2}})\). Finally, numerical experiments confirmed the numerical analysis of two-grid algorithm.

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Funding

The work of this author was supported by Natural Science Foundation of Guangdong province (2018A0303100016, 2018A030307024) and Educational Commission of Guangdong Province, China (2019KTSCX174).

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  1. School of Mathematics, Jiaying University, Meizhou, 514015, Guangdong, People’s Republic of China

    Hanzhang Hu

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  1. Hanzhang Hu
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Correspondence to Hanzhang Hu.

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Hu, H. Two-grid method for compressible miscible displacement problem by mixed finite element methods and expanded mixed finite element method of characteristics. Numer Algor 89, 611–636 (2022). https://doi.org/10.1007/s11075-021-01127-4

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