Department of Mathematical Sciences
Numerical Methods Seminar
Tuesday, October 28th, 2025
1:00PM-2:00PM
Stratton Hall 202
Speaker: Maurice Fabien, MIT
Title: A cell centered Galerkin method for miscible displacement in heterogeneous porous media
Abstract:
We present a cell centered Galerkin (CCG) method applied to miscible displacement problems in heterogeneous porous media. The CCG approach combines concepts from finite volume and discontinuous Galerkin (DG) methods to arrive at an efficient lowest-order approximation (one unknown per cell). We demonstrate that the CCG method can be defined using classical DG weak formulations, only requires one unknown per cell, and is able to deliver comparable accuracy (to piecewise linear DG) and improved efficiency over traditional higher-order interior penalty DG methods. An interesting feature of the CCG method is that it obeys a maximum principal property. A plethora of computational experiments in 2D and 3D showcase the effectiveness of the CCG method for highly heterogeneous flow and transport problems in porous media.