Mixed finite element approximations for Darcy flow of isentropic gases
- Aalif Biswas (Johns Creek High School, 5575 State Bridge Rd, Johns Creek, GA 30022)
- Aryan Bavera (Alliance Academy for Innovation, 1100 Lanier 400 Parkway, Cumming, GA 30040)
- Lynden Baek (North Gwinnett High School, 20 Level Creek Rd, Suwanee, GA 30024)
- Samhitha Kovi (Lambert High School, 805 Nichols Rd, Suwanee, GA 30024)
- Thinh Kieu (University of North Georgia)
- Tessica Selvaganesan (Lambert High School, 805 Nichols Rd, Suwanee, GA 30024)
Abstract
In this paper, the mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the single-phase Darcy flow of isentropic gas in a porous medium. Our numerical approach is based on the mixed finite element method (MFEM) in space, and backward-differences in time. The lowest order Raviart-Thomas elements are used. Within this frame work, we derive error estimates in suitable norms and show the convergence of the scheme. The features of the MFEM, especially of the lowest order Raviart- Thomas elements, are now fully exploited in the proof of convergence. Finally, we give the numerical experiments to confirm the theoretical analysis regarding convergence rates.
How to Cite:
Biswas, A., Bavera, A., Baek, L., Kovi, S., Kieu, T. & Selvaganesan, T., (2023) “Mixed finite element approximations for Darcy flow of isentropic gases”, North Carolina Journal of Mathematics and Statistics 9(1).
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