Yekaterina Epshteyn

Postdoctoral Associate at the Department of Mathematical Sciences and
Center for Nonlinear Analysis, Carnegie Mellon University


Numerical Analysis, Scientific Computing, Applied Mathematics  

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CV pdf

Brief Version of the Research Statement pdf

Research Interests:  

• Numerical Analysis, Scientific Computing, Applied Mathematics
• Finite Element Method: Continuous Galerkin (CG), Discontinuous Galerkin (DG)
• Central-Upwind Finite Volume Schemes
• Finite Difference Method, Difference Potentials Method
• Computational Fluid Dynamics
• Flow in Porous Media, Multiphase Flow
• Shallow Water Models
• Biomedical Applications
• Material Science Applications
• Optical tomography inverse problems

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.)

Publications

Teaching:  

• Spring 2010, Math 21-761: Numerical Methods for PDE: Finite Difference and Finite Volume Methods
• Fall 2009, Math 21-369: Numerical Methods
• Spring 2009, Math 21-369: Numerical Methods
• 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

Previous Teaching:

• 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)

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Contact Information

Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

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Last Modified: January 9, 2009