Maurice S. Fabien

Brown University, Providence College

Maurice S. Fabien has made significant contributions to various fields of study through recent research articles. In numerical analysis, they have developed an energy-stable HDG method for the Allen-Cahn equation, which enhances computational stability and accuracy. Additionally, their work on hybridization and postprocessing in finite element exterior calculus improves computational efficiency. Furthermore, fluid mechanics approaches were applied to analyze collagen fiber organization, while low-order divergence-free approximations were found for the Stokes problem on Worsey-Farin and Powell-Sabin splits. These advancements also led to the development of families of interior penalty hybridizable discontinuous galerkin methods and high-order implicit hybridizable galerkin methods for various applications in second-order elliptic problems and two-phase flow in heterogeneous porous media.