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A Mixed Finite Element Approximation of pre-Darcy Flows

Authors
  • Jiin Choi (Lambert High School, 805 Nichols Rd, Suwanee, GA 30024)
  • Dennis Garcia (Department of Mathematics, University of North Georgia, Gainesville Campus, 3820 Mundy Mill Rd., Oakwood, GA 30566, U.S.A.)
  • Thinh Kieu (University of North Georgia)
  • Roy Kim (Lambert High School, 805 Nichols Rd, Suwanee, GA 30024)
  • Ted Park (North Gwinnett High School, 20 Level Creek Rd, Suwanee, GA 30024)
  • Tessica Selvaganesan (Lambert High School, 805 Nichols Rd, Suwanee, GA 30024)

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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Published on
2024-10-15

Peer Reviewed

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Creative Commons Attribution 4.0