Yekaterina Epshteyn

Associate Professor at the Department of Mathematics
The University of Utah


Numerical Methods for PDEs, Scientific Computing, Applied Mathematics
 



CV pdf

Brief Version of the Research Statement pdf

Research Interests:  

  • Numerical Methods for PDEs, Scientific Computing, Applied Mathematics
  • Difference Potentials Method
  • Central-Upwind Finite Volume Schemes
  • Finite Element Methods
  • Mathematical and Computational Modeling of Materials
  • Computational Fluid Dynamics
  • Shallow Water Models
  • Flow in Porous Media, Multiphase Flow
  • Biomedical Applications

Gallery:

Some of the results that we obtained for two-phase flow simulation:
Below 2D view of saturation contour (left) and 3D view of pressure contour (right) at 350 days.
This is an example of heterogeneous benchmark problem (the permeability coefficient is discontinuous).
(Click on saturation picture to see the movie.)
pic1 pic2

Publications

  • REU Undergraduate Students:
      Alex Henabray (May 2014 - December 2014): Project "Numerical Solution of 1D Stefan Problem" (advised jointly with Jason Albright)
      Camille Humphries (May 2013 - May 2014): Project "Central-Upwind Schemes for Shallow Water Models" (in Fall 2013 and Spring 2014 advised jointly with Jason Albright)
  • PhD Graduate Students:
  • Alumni:

    Teaching:

    • Fall 2016, Math 6610: Analysis of Numerical Methods I
    • Fall 2016, Math 1311 : Accelerated Engineering Calculus I, Canvas
    • Spring 2016, Math 1320-009: Engineering Calculus II
    • Spring 2016, Math 1320-006: Engineering Calculus II
    • Fall 2015, Math 7875-008 : Selected Topics in Numerical Methods for PDE
    • Spring 2015, Math 6620 : Analysis of Numerical Methods II
    • Fall 2014, Math 6610 : Analysis of Numerical Methods I
    • Fall 2014, Math 1311 : Accelerated Engineering Calculus I
    • Spring 2014, REU Math 4800 : Undergraduate Research in Mathematics: Selected Numerical Algorithms and Their Analysis, Poster
    • Spring 2014, Math 5620 - Math 6865 : Introduction to Numerical Analysis II
    • Fall 2013, Math 1311 : Accelerated Engineering Calculus I
    • Spring 2013, Math 6630 : Numerical Solutions of Partial Differential Equations
    • Fall 2012, Math 5750 - Math 6880 : Optimization
    • Spring 2012, Math 6620 : Analysis of Numerical Methods II
    • Spring 2012, Math 6790 : Case Studies in Computational Engineering and Science: Mathematics and Materials
    • Fall 2011, Math 6610 : Analysis of Numerical Methods I
    • Spring 2011, Math 6620 :Analysis of Numerical Methods II
    • Fall 2010, Math 6610 : Analysis of Numerical Methods I

    Previous Teaching:

      Carnegie Mellon University:
    • Spring 2010, Math 21-761: Numerical Methods for PDE: Finite Difference and Finite Volume Methods (graduate course)
    • Fall 2009, Math 21-369: Numerical Methods (undergraduate course)
    • Spring 2009, Math 21-369: Numerical Methods (undergraduate course)
    • Fall 2008, Math 211-21: Integration and Differential Equations
    • Spring 2008, Math 211-21:Integration and Differential Equations
    • Fall 2007, Math 21-111:Calculus for Humanities Students I
    • University of Pittsburgh:
    • Teaching Assistant: Matrices and Linear Operators (Spring 2007)
    • Grader: Finite Element Method (Spring 2007)
    • Instructor: Calculus 1 (Summer 2005)
    • Teaching Assistant: Calculus 1, 2 (Spring 2004, 2005-2006)

    Contact Information

    Department of Mathematics
    The University of Utah
    Salt Lake City, UT 84112
    e-mail: epshteyn@math.utah.edu
    phone: (801) 585 - 1644


    Last Modified: December, 2015