2015/12/12 by Thinh Kieu, Kieu, Thinh
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1512.03951
openalex publication_date 2015/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we will consider the generalized Forchheimer flows for\nslightly compressible fluids. Using Muskat's and Ward's general form of\nForchheimer equations, we describe the fluid dynamics by a nonlinear degenerate\nparabolic equation for density. The long time numerical approximation of the\nnonlinear degenerate parabolic equation with time dependent boundary conditions\nis studied. The stability for all positive time is established in both a\ncontinuous time scheme and a discrete backward Euler scheme. A Gronwall's\ninequality-type is used to study the asymptotic behavior of the solution. Error\nestimates for the solution are derived for both continuous and discrete time\nprocedures. Numerical experiments confirm the theoretical analysis regarding\nconvergence rates.\n