The expanded upwind-mixed method on changing meshes for positive semi-definite problem of two-phase miscible flow

Abstract

The expanded upwind-mixed method on dynamically changing meshes is presented for the positive semi-definite problem of two-phase miscible flow in porous media. The pressure is approximated by a mixed finite element method and the concentration is approximated by a method which upwinds the convection and incorporates diffusion using an expanded mixed finite element method. When the mesh changes, error estimate is derived under the assumption of only a positive semi-definite diffusion coefficient. Finally, the numerical experiments are given.

Keywords:

• adaptive finite element method
• positive semi-definite
• upwind
• mixed finite element

2000 AMS Subject Classification :

• 65N30
• 65N12

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No.10372052, 10671060).