Mathematics Colloquium: Multiscale Finite Element Methods for Flows in Heterogeneous Porous Media and Applications
4:10 pm, Neill Hall 5W
Abstract: In this talk, I will describe multiscale finite element methods for flows in heterogeneous porous media. The main idea of multiscale finite element method is to construct finite element basis functions that can capture the small scale information.In particular, the small scale information is incorporated into the basis functions, which are coupled via global formulation of the problem. The basis functions can be simplified if there is scale separation. I will be mostly interested in heterogeneities that often arise in porous media applications (related to petroleum reservoirs) where one cannot assume scale separation. In this case, I will present an extension of multiscale finite element method that uses some type of limited global information to take into account the connectivity of the media. The method can be regarded as a reduced basis finite element method. I will also briefly mention the extension of the method to nonlinear partial differential equation (pseudo-monotone operators), the convergence results as well as homogenization results.