A Mixed Finite Element Approximation of pre-Darcy Flows
Abstract
In this paper, we consider the pre-Darcy flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stability of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. Numerical experiments confirm the theoretical analysis regarding convergence rates.
How to Cite:
Choi, J., Garcia, D., Kieu, T., Kim, R., Park, T. & Selvaganesan, T., (2024) “A Mixed Finite Element Approximation of pre-Darcy Flows”, North Carolina Journal of Mathematics and Statistics 10(1).
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