Giselle Saylor

gsosajones(at)oakland(dot)edu

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.

Contact me

Oakland University
Department of Mathematics and Statistics
Mathematics and Science Center
344 MSC
email: gsosajones at oakland dot edu

Research

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.

Research projects

  • Multiphase flow in porous media

  • Phase-field crystal modeling

  • Heat transfer due to radiation

Publications

Peer-reviewed

  1. G. Sosa Jones, M. Shillor, “A model for contact of a rod with an obstacle using the Damped Normal Compliance condition”. Submitted. 2024. Preprint

  2. G. Sosa Jones, C. Trenchea, “Discrete energy balance equation via a symplectic second-order method for two-phase flow in porous media”. Applied Mathematics and Computation, 480, 128909. 2024. Preprint

  3. 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

  4. 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

  5. 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

  6. 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.

  7. 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.

Theses

  1. G. Sosa Jones, “Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems” . Ph.D. Thesis, Applied Mathematics, University of Waterloo. 2020.

Teaching

Current - Fall 2024 (Oakland University)

APM 2555 Introduction to Differential Equations with Matrix Theory

  • Class hours: MoWeFr 9:20 am - 10:27 am at 242 EH
  • Office hours: MoWe 11:00 am - 12:00 pm at 344 MSC
  • See Moodle for course information

    • APM 4333/5333 Numerical Methods

  • Class hours: MoWe 3:30 pm - 5:17 pm at 364 MSC
  • Office hours: MoWe 11:00 am - 12:00 pm at 344 MSC
  • See Moodle for course information

    • Past

    Oakland University

    • MTH 1554 Calculus I: Fall 2022
    • MTH 2775 Linear Algebra: Winter 2023, Fall 2023
    • APM 4333/5333 Numerical Methods: Fall 2023
    • APM 4334/5334 Numerical Methods - Matrix Methods: Winter 2024
    • MTH 1221 Elementary functions and linear programming: Summer 2024

    University of Houston

    • Linear Algebra: Spring 2021, Summer 2021, Fall 2021, Spring 2022

    University of Waterloo

    • Linear Algebra for Engineering: Fall 2019

    Simón Bolívar University

    • Scientific Computing for Engineering: Summer 2016

    Talks

    Upcoming

    • Fall 2024 Finite Element Circus, University of Maryland, Baltimore County, Baltimore, MD, USA. October 18-19, 2024.

    Recent