Mathematical models used to describe porous medium flow lead to coupled systems of time-dependent nonlinear partial differential equations, which present serious mathematical and numerical difficulties. Standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid-orientation effect. The ELLAM-MFEM time-stepping procedure, in which an Eulerian–Lagrangian localized adjoint method (ELLAM) is used to solve the transport equation and a mixed finite element method (MFEM) is used for the pressure equation, simulates porous medium flow accurately even if large spatial grids and time steps are used. In this paper we prove an optimal-order error estimate for a family of ELLAM-MFEM approximations.
Published in Siam Journal of Numerical Analysis, Volume 46, Issue 4, 2008, pages 2133-2152.
© SIAM Journal On Numerical Analysis 2008, Society for Industrial and Applied Mathematics
Wang, H. (2008). An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow. SIAM Journal On Numerical Analysis, 46(4), 2133-2152. doi: 10.1137/s0036142903428281