Articles

A Mixed Finite Element Approximation of pre-Darcy Flows

Authors

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

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.

Keywords:

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).