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Publications
 V. John and S. Kaya, A Finite element variational multiscale
method for the Navier-Stokes equations, SIAM J. Sci. Comp 26., 1485-1503,
2005.
S. Kaya and B. Riviere, A
discontinuous subgrid eddy viscosity method for the time dependent Navier-
Stokes equations, SIAM J. Numer. Anal. 43, 1572-1595, 2005
S. Kaya and B. Riviere, A two-grid
stabilization method for solving the steady-State Navier-Stokes equations.
Numer. Meth. Part. Diff. Equations, 3(3), 728-743, 2006.
V. John, S. Kaya and W. J.
Layton, A two-level Variational Multiscale Method for Convection-Diffusion
Equations, Comp. Meth. Appl. Mech. Engrg., 195, 4594-4603, 2006.
S. Kaya, W. J. Layton and B.
Riviere, Subgrid Stabilized Defect Correction Methods for the Navier Stokes
Equations. SIAM J. Numer. Anal., 44(4), 1639-1654, 2006.
C. C. Manica and S. K. Merdan,
Finite Element Error Analysis of a Zeroth Order Approximate Deconvolution
Model Based in a Mixed formulation. J. Math. Anal. Appl. 331, 669-685,
2007,
V. John and S. Kaya, Finite element
error analysis of a variational multiscale method for the
Navier-Stokes equations. Adv.
Comput. Math., 28, 43-61,2008.
V. John, S. Kaya and A. Kindl,
"Finite Element Error Analysis for a Projection-Based Variational
Multiscale Method with Nonlinear Eddy Viscosity J. Math. Anal. Appl. 344,
627-641, 2008.
A. Cibik and S. Kaya, “A
projection based stabized finite element method for natural convection
problem. “ J. Math. Anal.
Appl. 381:2, 469-484, 2011.
S. Kaya and C. Manica, “ Convergence Analysis of the Finite Element Method for a Fundamental Model in Turbulence“, accepted for publication in M3AS, 2012.
Book: Numerical
Analysis of a Variational Multiscale Method for Turbulence, LAP LAMBERT
Academic Publishing, October 6, 2011,
Technical Reports
 S. Kaya Numerical analysis of a subgrid eddy
viscosity methods for higher Reynolds number flow problems, Technical
Report, TR-MATH 03-04,
University of Pittsburgh, 2003 .
 S. Kaya and W. J. Layton, Subgrid scale eddy
viscosity methods are variational multiscale method, Technical Report, TR-MATH 03-14, University of Pittsburgh, 2003 .
S. Kaya
and B. Riviere, Analysis of a discontinuous Galerkin and eddy viscosity
method for Navier Stokes
equations, Technical Report., TR-MATH 03-14,
University of Pittsburgh, 2003.
 V John and S. Kaya, Finite element error
analysis of a variational multiscale method for the Navier-Stokes
equations, Otto
–von- Guericke University, Magdeburg, 2003.
S. Kaya and B. Riviere, A two-grid
stabilization method for solving the steady-state Navier-Stokes equations,
Technical Report, TR-MATH
04-06, University of Pittsburgh, 2004.
 S. Kaya, W. J. Layton and B. Riviere, Subgrid
Stabilized Defect Correction Methods for the Navier Stokes Equations,
Technical Report, TR-MATH
05-01, University of Pittsburgh, 2005 .
 V. John, S. Kaya and W. J. Layton,
Algorithmic Issues in a Subgrid Scale Eddy Viscosity Method, Technical
Report, TR-MATH 05-02,
University of Pittsburgh, 2005
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