Abstract
Under the assumptions of nonlinear finite element and Δt =o(h), Ewing and Wheeler discussed a Galerkin method for the single phase incompressible miscible displacement of one fluid by another in porous media. In the present paper we give a finite element scheme which weakens the Δt =o(h)-restriction to Δt =o(H ε), 0 < ε ≤ 1/2. Furthermore, this scheme is suitable for both linear element and nonlinear element. We also derive the optimal approximation estimates for concentrationc, its gradient ∇c and the gradient ∇p of the pressurep.
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Li, Q., Chen, H. Finite element method for incompressible miscible displacement in porous media. Acta Mathematicae Applicatae Sinica 9, 204–212 (1993). https://doi.org/10.1007/BF02032915
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DOI: https://doi.org/10.1007/BF02032915