Journal Publications

  • Y.Epshteyn and S.Phippen, High-Order Difference Potentials Methods for 1D Elliptic Type Models, Volume 93, July 2015, pages 69-86, DOI: 10.1016/j.apnum.2014.02.005, Applied Numerical Mathematics, (Special Issue in Honor of Viktor Ryaben'kii 90th Birthday), pdf, and online
  • Y.Epshteyn, Algorithms Composition Approach based on Difference Potentials Method for Parabolic Problems, Communications in Mathematical Sciences, Volume 12 (2014), Number 4, pages 723 - 755, pdf, and online

  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, A Theory and Challenges for Coarsening in Microstructure, Springer INdAM Series "Analysis and Numerics of Partial Differential Equations" in Memory of Enrico Magenes, 2013, pdf, and online. Also CNA report 12-CNA-013 online

  • Y.Epshteyn, Upwind-Difference Potentials Method for Patlak-Keller-Segel Chemotaxis Model, Journal of Scientific Computing, Volume 53, Issue 3 (2012), Pages 689-713, pdf, and online

  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Critical events, entropy, and the grain boundary character distribution, Physical Review B, 83, 134117 2011, pdf , online ( This paper is selected by the editors of Physical Review B to be highlighted as an Editors' Suggestion and Featured in Physics: online )

    The accompanying Viewpoint on our paper by Robert V. Kohn: online

    About our work in SIAM News online

    Carnegie Mellon (CMU) News "Math-Made Materials" online

  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, An Entropy based theory of the grain boundary character distribution, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), Volume 30, Number 2, pages 427-454 June 2011, online. Also CNA report online (This paper is the part of a special issue dedicated to Louis Nirenberg on the occasion of his 85th Birthday ).

  • S. Bryson, Y. Epshteyn, A. Kurganov and G. Petrova, Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System, Mathematical Modelling and Numerical Analysis (M2AN) , 45 (2011) no. 3, pages 423-446, pdf, online, also CNA report 2008 , CNA report
  • Y. Epshteyn and A. Izmirlioglu, Fully Discrete Analysis of a Discontinuous Finite Element Method for the Keller-Segel Chemotaxis Model, Journal of Scientific Computing, Volume 40, Issue 1-3, 211-256, 2009, online
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer and S. Ta'asan, Geometric growth and character development in large metastable networks, Rendiconti di Matematica , Serie VII,Volume 29, Roma 2009, 65-81, pdf
  • B. Riviere, Y.Epshteyn, D.Swigon, Y.Vodovotz, A Simple Mathematical Model of Signaling Resulting from the Binding of Lipopolysaccharide with Toll-like Receptor 4 Demonstrates Inherent Preconditioning Behavior, Mathematical Biosciences, Volume 217, Issue 1, January 2009, pages 19-26, doi:10.1016/j.mbs.2008.10.002, 2008, online
  • Y. Epshteyn and A. Kurganov, New Interior Penalty Discontinuous Galerkin Methods for the Keller-Segel Chemotaxis Model, SIAM Journal on Numerical Analysis , Volume 47, no. 1, p.386-408, 2008, online
  • Y. Epshteyn, T.Khan and B. Riviere, Numerical Solution of A One-Dimensional Inverse Problem by The Discontinuous Galerkin method, Mathematics and Computers in Simulation, Volume 79, Issue 7, March 2009, pages 1989 - 2000, DOI:10.1016/j.matcom.2008.08.002, 2008
  • Y. Epshteyn, Discontinuous Galerkin Methods for the Chemotaxis and Haptotaxis Models, Journal of Computational and Applied Mathematics , Volume 224, no. 1, 168-181 2009
  • Y. Epshteyn and B. Riviere, Convergence of High Order Methods for Miscible Displacement, International Journal on Numerical Analysis and Modeling , Volume 5, Supp, p.47-63, 2008, online
  • Y. Epshteyn and B. Riviere, Analysis of hp Discontinuous Galerkin Methods for incompressible two-phase flow, Journal of Computational and Applied Mathematics , Volume 225, no. 2, 487-509 2009
  • Y. Epshteyn and B. Riviere, Estimation of penalty parameters for symmetric interior penalty Galerkin methods, Journal of Computational and Applied Mathematics , Volume 206, Issue 2, p. 843-872, 2007, online
  • Y. Epshteyn and B. Riviere, Fully implicit discontinuous finite element methods for two-phase flow, Applied Numerical Mathematics , Volume 57, Issue 4, p.383-401, 2007, online
  • V.S. Ryaben'kii, V. Turchaninov and Y. Epshteyn, Algorithm Composition Scheme for Problems in Composite Domains Based on the Difference Potential Method, Computational Mathematics and Mathematical Physics Translation from the original version published in Russian (published in "Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki") , Volume 46, Issue 10, p 1768-1784, 2006, online.

    Original Russian Version of the Paper online

  • Y. Epshteyn and B. Riviere, On the solution of incompressible two-phase flow by a p-version discontinuous Galerkin method, Communications in Numerical Methods in Engineering , Volume 22, Issue 7, pp.741-751, 2006, online
  • A. Dunca and Y.Epshteyn, On the Stolz-Adams deconvolution Model for the large-eddy simulation of turbulent flows, SIAM Journal on Mathematical Analysis , Volume 37, Issue 6, p 1890-1902, 2006, online
  • V.S. Ryaben'kii, V. Turchaninov and Y.Epshteyn, The numerical example of algorithms composition for solution of the boundary-value problems on compound domain based on Difference Potentials Method, Keldysh Institute for Applied Mathematics, Russia Academy of Sciences, N. 3, Moscow, 2003, online (Translation from the original version published in Russian and the order of the author's names in the paper is different since the Russian version of my last name starts with the letter which is almost the last letter of the alphabet)
Book Chapters

  • Scheme of algorithms composition based on difference potentials method (with V.S. Ryaben'kii and V. Turchaninov), in V.S. Ryaben'kii, " Difference Potentials Method and its Applications", Moscow, Russia, Fizmatlit 2010, Chapter 5, p. 290-311.
Conference Proceedings

  • R. Choksi, Y.Epshteyn and C. Liu, Mathematics of Multiscale and Multiphysics Phenomena in Materials Science, 24w5159, BIRS workshop 24w5159 final report, 2024, link, and pdf
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Recent Developments in Material Microstructure: A theory of Coarsening, Mater. Res. Soc. Symp. Proc. Vol. 1753, 2015 Materials Research Society, DOI: 10.1557/opl.2015.591 pdf
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Materials Microstructures: Entropy and Curvature-Driven Coarsening, in Research Institute of Mathematics, RIMS Proceedings, Kyoto University, 2013. also CNA report 13-CNA-003 online, and Proceedings
  • Y.Epshteyn, Upwind-Difference Potentials Method for Chemotaxis Models, proceedings of "European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)", 2012, pdf
  • Y.Epshteyn, Recent Developments in the Numerical Methods for the Chemotaxis Models, Oberwolfach report, EMS (European Mathematical Society) Volume 9, Issue 1, 2012, link, the proceedings of the workshop "Theory and Applications of Discontinuous Galerkin Methods", Mathematisches Forschungsinstitut Oberwolfach, Germany February 19-25 2012, pdf.
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Predictive theory for the grain boundary character distribution, in proceedings of " International Conference on Recrystallization and Grain Growth (REX GG 2010)", 2012, pdf
  • S.Bryson, Y.Epshteyn, A.Kurganov and G. Petrova, Central-Upwind Scheme on Triangular Grids for the Saint-Venant System of Shallow Water Equations, "The American Institute of Physics (AIP) Conference Series", Volume 1389, Issue 1, pp. 686-689, 2011, pdf
  • Y. Epshteyn, B. Riviere, D.Swigon, Y.Vodovotz, A Simple Mathematical Model of Lipopolysaccharide Signaling Through Toll-Like Receptor 4 Results in Complex Insights on Preconditioning, Journal of Critical Care, Volume 22, Issue 4, 2007, proceedings of " 6th International Conference on Complexity in Acute Illness", October 4-7 2007.
  • Y. Epshteyn and B. Riviere, Fully Implicit Discontinuous Galerkin Scheme for Two-Phase Flow, in the proceedings of MSRI Conference "The Legacy of Ladyzhenskaya and Oleinik" May 17-21 2006 , online.
Selected Reports

  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Materials Microstructures: Entropy and Curvature-Driven Coarsening, CNA report 13-CNA-003 online
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, An Entropy based theory of the grain boundary character distribution, CNA report 11-CNA-001 2011 , online
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Critical Events, Entropy, and the Grain Boundary Character Distribution, CNA report 10-CNA-014 2010 , online.
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Predictive Theory for the Grain Boundary Character Distribution, CNA report 10-CNA-013 2010 , online .
  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer and S. Ta'asan, Geometric growth and character development in large metastable networks, CNA report 08-CNA-025 2008 , online .
  • S. Bryson, Y. Epshteyn, A. Kurganov and G. Petrova, Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System, CNA report 2008 , online.