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Publications
 PhD Thesis: Numerical
Analysis of a Variational Multiscale Method for Turbulence, University
of Pittsburgh, December 2004. This thesis is selected as 2004 HALES DISTINGUISHED RESEARCH AWARD for the
Best Doctoral Dissertation.
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, “Numerical Analysis of Stabilized Finite Element Method for
Natural Convection Problem”, submitted 2010
A. Cibik and
S. Kaya, “Stabilized Finite Element
for Time-Dependent Natural Convection Problem”, In preparation
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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