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


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


  • REU Undergraduate Students:
      Gabrielle Legaspi (Summer 2017): Introduction to Research
      Alex Henabray (Fall 2014): Project "Numerical Methods for Interface Problems"
      Camille Humphries (May 2013 - May 2014): Project "Central-Upwind Schemes for Shallow Water Models"
  • PhD Graduate Students:
  • Alumni:
      Spencer Phippen (REU student, May 2013 - January 2014): Project "Difference Potentials Method for Interface Problems", Current Position: Software Engineer at Google
      Jason Albright (Ph.D. student Fall 2011 - Spring 2016), Current Position: Postdoctoral Fellow at the Theoretical Division at Los Alamos National Lab (LANL)
      Patrick Bardsley (Ph.D. student Fall 2011 - Spring 2016, Ph.D. thesis abstract ), Current Position: Postdoctoral Fellow at the Department of Mathematics and ICES at the University of Texas at Austin
      Michael Medvinsky (Postdoc, Fall 2013 - Spring 2015), Current Position: Research Assistant Professor, Department of Mathematics, North Carlina State University

  • Recent Research Talks to Middle School Students, Spring 2013:

    Project Youth - University of Utah (for 6th Graders from local schools), Spring 2013, Slides

    The presentation "Fun Adventure in Applied Mathematics or What is Applied Mathematics?" was illustrated by experiments:
  • Generating waves in a pan with a whole milk
  • And experiments using soap bubbles

  • Applied Math Seminar, Spring 2018, html

    MAC Website html

    Affiliated Faculty Member, Center for Quantitative Biology, html

    Some Selected Recent Conferences:

    International Conference "Difference Schemes and Applications" in honor of 90th Birthday of Prof. Viktor Ryaben'kii, Moscow, Russia, May 27-31 2013, Program

    ICOSAHOM 2014 , International Conference on Spectral and High Order Methods, Salt Lake City, Utah, June 23-27 2014

    CMDS 13, Continuum Models Discrete Systems, Salt Lake City, Utah, July 21-25 2014

    WhAM! A Research Collaboration Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations, IMA Special Workshop, Minneapolis, August 11-15 2014

    IMA Hot Topic Workshop "Impact of Waves Along Coastlines" , Minneapolis, October 2014

    Prairie Analysis Seminar, Kansas State University, September 2015

    International Conference "Topics in Applied Nonlinear Analysis: Recent Advances and New Trends" in honor of 75th Birthday of Prof. David Kinderlehrer, Carnegie Mellon University, July 2016

    Current Teaching:

    Contact Information

    Department of Mathematics
    The University of Utah
    Salt Lake City, UT 84112
    phone: (801) 585 - 1644

    Last Modified: October, 2017