Journal Publications

  • Y.Epshteyn, Algorithms Composition Approach based on Difference Potentials Method for Parabolic Problems, Communications in Mathematical Sciences, in revision (submitted), pdf
  • 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

  • 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, B 83, 134117 2011 online ( This paper is selected by the editors of Physical Review B to be highlighted as an Editors' Suggestion: online )

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

    About our work in SIAM News 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, 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 pdf, 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 , also 08-CNA-026 CNA report.
  • 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 , 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, 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 , 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 , 224, no. 1, 168-181 2009, gzip.
  • 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.
  • Y. Epshteyn and B. Riviere, Analysis of hp Discontinuous Galerkin Methods for incompressible two-phase flow, Journal of Computational and Applied Mathematics , 225, no.2,487-509 2009, online
  • Y. Epshteyn and B. Riviere, Estimation of penalty parameters for symmetric interior penalty Galerkin methods, Journal of Computational and Applied Mathematics , Volume 206, p.843-872, 2007, pdf.
  • Y. Epshteyn and B. Riviere, Fully implicit discontinuous finite element methods for two-phase flow, Applied Numerical Mathematics , Volume 57, p.383-401, 2007, online
  • Y. Epshteyn, V.S. Ryaben'kii and V. Turchaninov, Scheme of algorithms composition based on 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") 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) , Volume 10, p 1768-1784, 2006, pdf.

    Original Russian Version of the Paper pdf .

  • 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.
  • Y. Epshteyn, V.S. Ryaben'kii and V. Turchaninov, The numerical example of algorithms composition for solution of the boundary-value problems on compound domain based on difference potential method, Keldysh Institute for Applied Mathematics, Russia Academy of Sciences, N. 3, Moscow, 2003.
Book Chapters

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

  • K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta'asan, Materials Microstructures: Entropy and Curvature-Driven Coarsening, to appear in Research Institute of Mathematics, RIMS Proceedings, Kyoto University, January 2013, pdf. Also CNA report 13-CNA-003 online

  • Y.Epshteyn, Upwind-Difference Potentials Method for Chemotaxis Models, submitted to 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 10/2012, p.10-12, the proceedings of the workshop "Theory and Applications of Discontinuous Galerkin Methods", Mathematisches Forschungsinstitut Oberwolfach, Germany February 19-25 2012, , 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, 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.
Non-Refereed Conference Proceedings

  • 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.
Reports

  • 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.
  • Y. Epshteyn and A.Kurganov, New Discontinuous Galerkin Methods for the Keller-Segel Chemotaxis Model, CNA report 2007 , online.
  • Y. Epshteyn and B. Riviere, High Order Fully Discrete Discontinuous Galerkin Methods for Miscible Displacement, CNA report 2007 , online.