Abstract
In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank–Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart of the analysis is the proof of convergence under low regularity requirements. Numerical experiments demonstrate that the proposed method exhibits second-order convergence for smooth and robustness for rough problems.
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References
S. Bartels, M. Jensen, R. Müller, Discontinuous Galerkin finite element convergence for incompressible miscible displacement problems of low regularity, SIAM J. Numer. Anal. 47(5):3720–3743, 2009
Z. Chen, Reservoir simulation (Mathematical techniques in oil recovery), SIAM, 2007
X. Feng, Recent developments on modeling and analysis of flow of miscible fluids in porous media, Fluid flow and transport in porous media, Contemp. Math. 295:229–224, 2002
B. Rivière, N. Walkington, Convergence of a Discontinuous Galerkin Method for the Miscible Displacement Equations Under Minimal Regularity, 2009, http://www.math.cmu.edu/\~noelw/Noelw/Papers/RiWa09.pdf
V. Thomée, Galerkin finite element methods for parabolic problems, Springer Series in Computational Mathematics 25, 1997
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Jensen, M., Müller, R. (2010). Stable Crank–Nicolson Discretisation for Incompressible Miscible Displacement Problems of Low Regularity. In: Kreiss, G., Lötstedt, P., Målqvist, A., Neytcheva, M. (eds) Numerical Mathematics and Advanced Applications 2009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11795-4_50
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DOI: https://doi.org/10.1007/978-3-642-11795-4_50
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