Typical porous media processes are affected by heterogeneities at different length scales. In this talk, I will describe multiscale finite element methods for flow and transport in heterogeneous porous media. The main focus of the talk is on subgrid capturing using various local and global methods.

I will discuss the use of local boundary conditions and the use of global information in capturing subgrid effects. The upscaling of the transport equation and its coupling to the flow equation will be presented. The mathematical analysis of these methods will be discussed.