DMS Applied Math Seminar

Speaker: Prof. Sanghyun Lee (Florida State University)

Title: Enriched Galerkin Finite Element Methods for Coupling Flow and Transport in Porous Media

Abstract: We present and analyze enriched Galerkin finite element methods (EG) to solve coupled flow and transport system in porous media such as viscosity and density-driven flows. The EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. This approach is shown to be locally and globally conservative while keeping fewer degrees of freedom in comparison with discontinuous Galerkin finite element methods (DG). Linear solvers and dynamic mesh adaptivity techniques using entropy residual and hanging nodes will be discussed. Some numerical tests in two and three dimensions are presented to confirm our theoretical results as well as to demonstrate the advantages of the EG.