Yuan, Yirang; Wang, Wenqia; Yang, Danping Finite element methods and numerical analysis for petroleum origin and accumulation in basin evolution. (Chinese. English summary) Zbl 0830.76054 J. Syst. Sci. Math. Sci. 14, No. 1, 9-20 (1994). Summary: Petroleum origin and accumulation in basin evolution are governed by a system of nonlinear partial differential equations. The mathematical model considered here comprises: (1) fluid flow; (2) heat transport; (3) porosity of the media. The pressure, Darcy velocity, and temperature are approximated by the finite element method. Optimal order convergence in \(L^2\) and \(H^1\) is proved. MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage 86A20 Potentials, prospecting 80A20 Heat and mass transfer, heat flow (MSC2010) 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:optimal order convergence; Darcy velocity PDFBibTeX XMLCite \textit{Y. Yuan} et al., J. Syst. Sci. Math. Sci. 14, No. 1, 9--20 (1994; Zbl 0830.76054)