An Optimal-Order Estimate for MMOC-MFEM Approximations to Porous Medium Flow

作者：Wang Kaixin^*

来源：Numerical Methods for Partial Differential Equations, 2009, 25(6): 1283-1302.

DOI：10.1002/num.20397

• advection-diffusion equations
• characteristic methods
• convergence analysis
• error estimates
• numerical analysis
• porous medium flow

Mathematical models used to describe porous medium flow lead to coupled systems of time-dependent partial differential equations. Standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid-orientation effect. The MMOC-MFEM time-stepping procedure, in which the modified method of characteristics (MMOC) 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 article we prove an optimal-order error estimate for a family of MMOC-MFEM approximations.

• 出版日期2009-11
• 单位山东大学