Mathematics Seminar 03/03/23

Abstract: We propose a low-cost, parameter-free, and pressure-robust Stokes solver based on the enriched Galerkin (EG) method with a discontinuous velocity enrichment function. The EG method employs the interior penalty discontinuous Galerkin (IPDG) formulation to weakly impose the continuity of the velocity function. However, the symmetric IPDG formulation, despite its advantage of symmetry, requires a lot of computational effort to choose an optimal penalty parameter and to compute different trace terms. In order to reduce such effort, we replace the derivatives of the velocity function with its weak derivatives computed by the geometric data of elements. Therefore, our modified EG (mEG) method is a parameter-free numerical scheme which has reduced computational complexity as well as optimal rates of convergence. Moreover, we achieve pressure-robustness for the mEG method by employing a velocity reconstruction operator on the load vector on the right-hand side of the discrete system. The theoretical results are confirmed through numerical experiments with two- and three-dimensional examples. (This is joint work with Prof. Lin Mu.)

Biosketch: Dr. Lee obtained his PhD degree from University of California, Irvine (2015 – 2021), his Master (2013 – 2015) and Bachelor (2006 – 2013) degrees from Yonsei University, Seoul. He is currently a limited term assistant professor in the department of mathematics at University of Georgia. His research interests are in numerical analysis, finite element methods (FEMs), numerical partial differential equations (PDEs), and optimization problems.