Abstract: We present and analyze enriched Galerkin finite element methods (EG) to solve coupled system in porous media such as flow, transport, and Biot system. 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.
Bio: Dr. Sanghyun Lee is an assistant professor in the Department of Mathematics at Florida State University. He was a postdoctoral fellow then a research associate in the Center for Subsurface Modeling, Institute of Computational Engineering and Science at the University of Texas at Austin. He received his Ph.D. in mathematics from Texas A&M University. His research interests are focused on design, analysis, and implementation of numerical methods for partial differential equations (PDEs). Especially, he is interested in coupling mechanics, flow, and transport problems in subsurface, which requires coupling multiple PDEs. His expertise lies on physics preserving numerical methods for these coupled multiphysics and multi-scale problems.