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A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem

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Abstract

A compressible miscible displacement problem is modeled by a nonlinear coupled system with partial differential equations in porous media. A two-grid algorithm of a combined mixed finite element and discontinuous Galerkin approximation is proposed based on the Newton iteration method. The error estimate in \(H^1\)-norm for concentration and the error estimate in \(L^2\)-norm for velocity are derived. It is shown that an asymptotically optimal approximation rate with the two-grid algorithm can be achieved if \(h = O(H^{2})\) is satisfied, where H and h are mesh sizes of the coarse grid and the fine grid, respectively. Numerical experiments indicate that the two-grid algorithm is effective, which coincides the theoretical analysis.

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Funding

This work was supported by Project funded by Hunan Provincial Natural Science Foundation of China (Grant No. 2020JJ4242, 2021JJ30178), Scientific Research Fund of Hunan Provincial Education Department (Grant No. 21C0585).

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  1. College of Science, Central South University of Forestry and Technology, Changsha, 410004, Hunan, China

    Jiming Yang & Jing Zhou

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  1. Jiming Yang
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Yang, J., Zhou, J. A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem. Numer Algor 94, 733–763 (2023). https://doi.org/10.1007/s11075-023-01518-9

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