I am an Assistant Professor in the Department of Mathematics and Statistics at Oakland University, Michigan. Previously, I was a Postdoctoral Researcher in the Department of Mathematics at the University of Houston where I worked with Dr. Loic Cappanera. In 2020, I obtained my Ph.D. in Applied Mathematics at the University of Waterloo in Canada under the supervision of Dr. Sander Rhebergen.
My research interests lie in the design of finite element discretizations for the solution of partial differential equations with applications to realistic and challenging problems in science and engineering. For my projects, I implement novel discretization methods using open-source parallel codes to produce accurate and realistic simulations. Furthermore, I analyze the theoretical convergence of the methods under consideration, which involves rigorous mathematical proofs.
Multiphase flow in porous media
Free-surface waves
Welding plate problems
G. Sosa Jones, C. Trenchea, “Discrete energy balance equation via a symplectic second-order method for two-phase flow in porous media”. Submitted. 2023. Preprint
G. Sosa Jones, B. Riviere, L. Cappanera, “Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media” . IMA Journal of Numerical Analysis, 43:5, pp 2714–2747, 2023. Preprint
G. Sosa Jones, S. Rhebergen, “An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows” . Computers & Fluids, 246, 105625. 2022. Preprint
G. Sosa Jones, J.J. Lee, S. Rhebergen, “A space-time hybridizable discontinuous Galerkin method for linear free-surface waves” . Journal of Scientific Computing, 85:61. 2020. Preprint
G. Sosa Jones, J. Arteaga, O. Jiménez, “A study of mimetic and finite difference methods for the static diffusion equation” . Computers & Mathematics with Applications, 76/3, pp 633-648. 2018.
S. Buitrago, G. Sosa Jones, O. Jiménez, “An Upwind Finite Volume Method on Non-Orthogonal Quadrilateral Meshes for the Convection Diffusion Equation in Porous Media” . Applicable Analysis: An International Journal (Taylor & Francis Production), 95/10, pp 2203-2223. 2015.
G. Sosa Jones, “Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems” . Ph.D. Thesis, Applied Mathematics, University of Waterloo. 2020.
APM 4334/5334 Numerical Methods: Matrix Methods (Winter 2024)
Oakland University
University of Houston
University of Waterloo
Simón Bolívar University