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:
      Alex Henabray (May 2014 - current): 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)
      Spencer Phippen (May 2013 - January 2014): Project "Difference Potentials Method for Interface Problems", Recipient of Susan C. Christiansen Memorial Scholarship, April 2014
  • PhD Graduate Students:
      Jason Albright (Spring 2012 - present), Recipient of the Outstanding Graduate Student Award, April 2014
      Recipient of the SIAM Travel Award to attend and to present together with Qing Xia their work at "International Congress on Industrial and Applied Mathematics" ICIAM 2015, Beijing, China, August 10-14 2015
      Recipient of the University of Utah Graduate Research Fellowship, 2015-2016
      Patrick Bardsley (Spring 2012 - present), Recipient of Rushing Research Fellowship, April 2015
      Kyle Steffen (Fall 2013 - present, co-advised with K. Golden)
      Qing Xia (Fall 2014 - current)
  • Postdoc:

  • 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, Fall 2015, html

    Applied Math Seminar, Spring 2015, html

    Applied Math Seminar, Fall 2014, html

    Applied Math Seminar, Spring 2014, html

    Applied Math Seminar, Fall 2013, html

    MAC Website html

    Affiliated Faculty Member, Center for Quantitative Biology, html

    Some Recent and Future 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 Topics Workshop: Impact of Waves Along Coastlines, Minneapolis, October 14-17 2014, Poster

    Pacific Northwest Numerical Analysis Seminar, PNWNAS, October 18 2014

    CMDS Investigators Workshop: At the Frontiers of Computation and Materials, Snowbird, Utah, May 16 2015

    Thirteenth Prairie Analysis Seminar, Kansas State University, September 25-26, 2015


    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
    phone: (801) 585 - 1644

    Last Modified: July, 2015