Special Session 108: New Developments in porous media

An expanded mixed FEM for generalized Forchheimer flows of slightly incompressible fluids in porous media

Thinh Kieu
University of North Georgia
Co-Author(s):    Akif Ibragimov
We study the expanded mixed finite element method applied to the generalized Forchheimer equation with the Dirichlet boundary condition. The bounds for the solutions are established. In both continuous and discrete time procedures, utilizing the monotonicity properties of Forchheimer equation and boundedness of solutions, we establish the error estimates for the solutions in several Lebesgue norms. A numerical example using the lowest order Raviart-Thomas ($RT_0$) mixed element agrees our theoretical result regarding convergence rate.