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28 July 2023 Convergence analysis for expanded mixed finite element method and corresponding nine point cell-centered finite difference method for compressible miscible displacement in heterogeneous porous media I
Xinyu Zhang, Yongqiang Ren
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Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275641 (2023) https://doi.org/10.1117/12.2686460
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China
Abstract
In this paper, based on the Extended Mixed Finite Element Method (EMFEM), we discretize the pressure equation with full tensor permeability, which is often derived by applying upscaling technique to the huge geological grid model or in the heterogeneous porous medium case. We apply traditional Finite Element Method (FEM) to solve the concentration equation. We prove the optimal order convergence rate of the numerical solution of pressure p and concentration c in L2 - norm.
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Xinyu Zhang and Yongqiang Ren "Convergence analysis for expanded mixed finite element method and corresponding nine point cell-centered finite difference method for compressible miscible displacement in heterogeneous porous media I", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275641 (28 July 2023); https://doi.org/10.1117/12.2686460
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KEYWORDS
Finite element methods
Finite difference methods
Numerical analysis
Error analysis
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