Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Friday, April 9, 2021 - 12:00 to 13:00

Speaker Info

University of Texas El Paso

In this talk, we consider a new finite element method for solving Biot's equations that model the coupled fluid and mechanics in deformable porous media. The primary purpose of the study is to develop a computationally efficient and robust numerical method that is free of both pressure oscillations and volumetric locking. The method utilizes a new locking-free enriched Galerkin method for the displacement of the solid phase and a locally conservative enriched Galerkin method for the pressure of the fluid phase. These EG methods utilize the well-known discontinuous Galerkin (DG) techniques, but the approximation spaces have fewer degrees of freedom than those for the typical DG methods, thus offering an efficient alternative to DG methods. We present a priori error estimates of optimal order. We also demonstrate through some numerical examples that the new method is free of pressure oscillations and volumetric locking and can even handle well the heterogeneity of porous medium.

BIO: Dr. Son-Young Yi is an Associate Professor of Mathematics at the University of Texas at El Paso (UTEP). She received her Ph.D. in Mathematics from Purdue University in 2006 under the supervision of the late Professor Jim Douglas, Jr. Then, she joined Oregon State University as a postdoctoral research associate under the guidance of Drs. Ralph Showalter and Malgorzata Peszynska. After completing her postdoctoral training for three years, she was appointed to the Department of Mathematical Sciences at UTEP as an Assistant Professor in 2009. She was later promoted to an Associate Professor in 2015. Dr. Yi’s areas of expertise include the numerical analysis of partial differential systems, mathematical modeling, and scientific computation. Her research includes the modeling of multiscale, multiphase flow in porous media, computational solid mechanics and fluid mechanics, Eulerian-Lagrangian schemes for advective transport, and computational finance. Dr. Yi currently serves as the Treasurer of the SIAM TX-LA section and as the Director of the Graduate Certificate Program in Applied and Computational Mathematics at UTEP.