G.A. Baker,V.A. Dougalis and O. Karakashian,``On Multistep-Galerkin
discretizations of semilinear hyperbolic and parabolic equations'',
Jour. of Nonlinear Analysis, Vol. 4, No. 3, 1980, pp. 579-597.
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O. Karakashian, ``On a Galerkin-Lagrange Multiplier method for the
stationary Navier-Stokes equations''. SIAM. J. Numer. Anal., Vol. 19,
No. 5, 1982, pp. 909-923.
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G.A. Baker,V.A. Dougalis and O. Karakashian,``On a higher order acurate
fully discrete Galerkin approximation to the Navier-Stokes equations'',
Math. Comp., Vol. 39, No. 160, 1982, pp. 339-375.
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G.A. Baker,V.A. Dougalis and O. Karakashian,``Convergence of Galerkin
approximations for the Korteeweg-de Vries equation'',
Math. Comp.,Vol. 40, No. 162, 1983, pp. 419-433.
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V.A. Dougalis and O. Karakashian, ``On higher order accurate fully
discrete Galerkin aproximations for the Korteweg-de Vries equation''
Math. Comp., Vol. 45, No. 172, 1985, pp. 329-345.
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J.L. Bona and V.A. Dougalis and O. Karakashian, ``Fully discrete
Galerkin methods for the Korteweg-de Vries equation'',
Computers & Maths. with Appls., Vol. 12, No. 7, Part A, 1986, pp. 859-884.
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O. Karakashian, ``Galerkin single-step methods for second order
hyperbolic equations'', Computers & Maths. with Appls., Vol. 12, Nos. 4-5, Part A,
1986, pp. 605-613.
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O. Karakashian, ``On Runge-Kutta methods for parabolic problems with
time-dependent coefficients'', Math. Comp., Vol. 47, No. 175, 1986,
pp. 77-101.
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O. Karakashian, ``On Runge-Kutta-Nystrom methods for hyperbolic problems
with time-dependent coefficients'', Computers & Maths. with Appls., Vol. 13,
Nos. 9-11, Part A, 1987, pp. 785-800.
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L.A. Bales, S.M. Serbin and O. Karakashian, ``On the $A_0$-acceptability of
rational approximations to the exponential function with only real
poles'', BIT, Vol. 28, No. 1, 1988, pp. 69-79.
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L.A. Bales, S.M. Serbin and O. Karakashian, ``On the stability of
rational approximations to the cosine with only imaginary poles'',
BIT, Vol. 28, No. 3, 1988, pp. 651-658.
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O. Karakashian and W. Rust, ``On the parallel implementation of implicit
Runge-Kutta methods'', SIAM J. Sci. Stat. Comput., Vol. 9, No. 6, 1988,
pp. 1085-1090.
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G.A. Baker, W.N. Jureidini and O. Karakashian, ``Piecewise solenoidal
vector fields and the Stokes problem'', SIAM J. Numer. Anal., Vol. 27,
No. 6, 1990, pp. 1466-1485.
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D.G. Cacuci and O. Karakashian, ``Benchmarking the propagator method for
nonlinear systems: A Burgers-Korteweg-de Vries equation'', J. of Comp.
Phys., Vol. 89, No. 1, 1990, pp. 63-79.
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O. Karakashian and W. McKinney, ``On optimal high order in time
approximations for the Korteweg-de Vries equation'', Math. Comp.,
Vol. 55, No. 192, 1990, pp. 473-496.
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J.L. Bona, V.A. Dougalis, O. Karakashian and W. McKinney, ``Fully discrete methods with grid refinement for the Generalized Korteweg-de Vries equation'', Proceedings of the workshop on viscous and numerical approximations of shock waves. N.C. State University, May 1990, Michael Shearer ed.
G. Akrivis and V.A. Dougalis and O. Karakashian, ``Crank-Nicolson-Galerkin
finite element methods for the nonlinear Schr\"odinger equation'',
Numer. Mathematik, Vol. 59, No. 1, 1991, pp. 31-53.
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J.L. Bona, V.A. Dougalis, O. Karakashian and W. McKinney, ``Numerical solution of the Generalized Korteweg-deVries-Burgers equation with adaptive Galerkin methods'', Proceedings of the 1st national Congress on Computational Mechanics. Athens,Greece,Sept 3-4,1992, D.Beskos ed.
J.L. Bona, V.A. Dougalis, O. Karakashian and W. McKinney, ``Computations of blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation'', in Applied Numerical Mathematics, 10(1992), pp. 335-355.
G.D. Akrivis, V. A. Dougalis, O. Karakashian and W. McKinney, ``Galerkin-finite element methods for the Nonlinear Schr\"odinger equation'', in Hellenic Research in Mathematics and Informatics, ed. by E.A. Lipitakis, Hellenic Mathematical Society, 1992, pp. 421-442.
G. Akrivis and V.A. Dougalis and O. Karakashian, ``Numerical methods for the Nonlinear Schr\"o-dinger equation'', in Advances in Computer Methods For Partial Differential Equations VII, R. Vichnevetsky, D. Knight and G. Richter eds. IMACS, 1992, pp.1-7.
O. Karakashian, G. Akrivis and V. Dougalis, ``On optimal high order
estimates for the nonlinear Schr\"odinger equation'', SIAM J. Numer.
Anal., Vol. 30, No. 2, 1993, pp. 377-400.
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O. Karakashian and W. McKinney, ``On the approximation of solutions of the Generalized Korte-weg-de Vries-Burgers equation'', Mathematics and Computers in Simulation, 37(1994) pp. 405--416.
J.L. Bona, V.A. Dougalis, O. Karakashian and W. McKinney, ``Conservative
high order schemes for the Generalized Korteweg-de Vries equation'',
Phil. Trans. of Roy. Soc. of London A, Vol. 351, No. 1695, 1995,
pp. 107--164.
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J.L. Bona, V.A. Dougalis, O. Karakashian and W. McKinney, ``The effect of dissipation on the evolution of solutions of the Generalized Korteweg-de Vries equation'', Jour. of Comput. and Applied Math. 74 (1996), pp. 127--154.
J.L. Bona, V.A. Dougalis, O. Karakashian and W. McKinney, ``Numerical simulation of singular solutions of the Generalized Korteweg-de Vries equation'', Contemporary Mathematics, Vol 200(1996), pp.17--29.
G. Akrivis, V. Dougalis and O. Karakashian, ``Solving the system of equations arising in the discretization of some nonlinear pde's by implicit Runge-Kutta methods'', RAIRO MMAN,31 (1997), pp. 251--288.
O. Karakashian and W. Jureidini, ``A nonconforming finite element method
for the Stationary Navier-Stokes Equations'', SIAM J. Numer. Anal.,
Vol. 35, No. 1, 1998, pp. 93--120.
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O. Karakashian and C. Makridakis, ``A space-time finite element method
for the nonlinear Schr\"o- dinger equation: The discontinuous Galerkin
method'', Math. Comp., Vol. 67, No. 222, 1998, pp. 479--499.
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G. Akrivis, V. Dougalis, O. Karakashian and W. McKinney, ``Numerical approximation of singular solutions of the damped nonlinear Schr\"odinger equation'', Proceedings of the ENUMATH 97, 2nd European conference on numerical mathematics and advanced applications, H.G.Bock, F.Brezzi, R.Glowinski, G.Kanschat, Y.A.Kuznetsov, Periaux, R.Rannacher eds. World Scientific, Singapore 1998, pp.117--124.
O. Karakashian and C. Makridakis, ``A space-time finite element method
for the nonlinear Schr\"o- dinger equation: The continuous Galerkin
method'', SIAM J. Numer. Anal., Vol. 36, No. 6, 1999, pp.1779--1807.
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O. Karakashian and T. katsaounis, ``A discontinuous Galerkin method for the incompressible Navier-Stokes equations'', In the proceedings of the International Symposium on the discontinuous Galerkin method, B. Cockburn, G.E. karniadakis, C.-W. Shu Eds., Springer lecture notes in Computational Science and Engineering, 1999, pp.157--166.
X. Feng and O. Karakashian, ``Two-level Additive Schwarz methods for a
discontinuous Galerkin approximation of second-order elliptic problems'',
SIAM J. Numer. Anal., Vol. 39, No. 4, 2001, pp. 1343--1365.
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X. Feng and O. Karakashian, ``Analysis of two-level overlapping Schwarz preconditioners for a discontinuous Galerkin method'', In the proceedings of the thirteenth international conference of domain decomposition methods. N. Debit, M. garbey, R. Hoppe, J. periaux, D. keyes and Y. Kuznetsov eds., Domain Decomposition Press, Bergen Norway, 2001, pp. 235--243.
S.S. Gleason, H. Sari-Sarraf, M.A. Abidi, O. Karakashian and F. Morandi,`` A new deformable model for analysis of X-Ray CT images in preclinical studies of mice for polycystic kidney disease'', IEEE transactions on medical imaging, Vol. 21, No. 10, Oct. 2002, pp. 1302--1309.
G. Akrivis, O. Karakashian and F. Karakatsani,``Linearly implicit methods
for nonlinear evolution equations'', Numer. Mathematik, Vol. 94, No. 3,
2003, pp. 403--418.
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G. Akrivis, V. Dougalis, O. Karakashian and W. McKinney, ``Numerical
approximations of blow-up of radially symmetric solutions of the
nonlinear Schr\"odinger equation'', SIAM J. Sci. Comput., Vol. 25, No. 1,
2003, pp. 186--212.
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O. Karakashian and F. Pascal, ``A-posteriori error estimates for a
discontinuous Galerkin approximation of second order elliptic problems'',
SIAM J. Num. Anal., Vol. 41, No. 6, 2003, pp. 2374--2399.
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O.Karakashian and C. Makridakis, ``Convergence of a continuous
Galerkin method with mesh modification for nonlinear wave
equations'', Math. Comp., Vol. 74, No. 249, 2005, pp. 85--102.
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O. Karakashian and F. Pascal,``Adaptive discontinuous Galerkin
approximations of second-order elliptic equations",In Proceedings of
the European Congress on Computational Methods in Applied Sciences and
Engineering, ECCOMAS 2004. P. Neittaanma\"{a}ki et al. eds.,
Jyv\"{a}skyl\"{a}, Finland, July 24-28, 2004.
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X. Feng and O. Karakashian, ``Two-level non-overlapping Schwarz
preconditioners for a discontinuous Galerkin approximation of the
biharmonic equation", J. of Sci. Comput., Vol. 22, No. 1, 2005,
pp. 289--314.
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O. Karakashian and T. Katsaounis, ``Numerical simulation of incompressible
fluid flow using locally solenoidal elements". Comps. and Maths. with
Appls., Vol. 51, Nos. 9-10, 2006, pp. 1551--1570.
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O. Karakashian and F. Pascal, ``Convergence of adaptive discontinuous
Galerkin approximations of second-order elliptic problems". SIAM J.
Numer. Anal., Vol. 45, No. 2, 2007, pp. 641--665.
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X. Feng and O. Karakashian, ``Fully Discrete Dynamic Mesh Discontinuous
Galerkin Methods for the Cahn-Hilliard Equation of Phase Transition''.
Math. Comp., Vol. 76, No. 259, 2007, pp. 1093--1117.
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O. Karakashian," On an approximation result for piecewise polynomial functions". In Proceedings of the M3ST'09 conference, Bull. of Greek Math. Soc., Vol 57, 2010, pp. 221--227.
J.L. Bona, H. Chen, O. Karakashian and Y. Xing, ``Conservative,
discontinuous-Galerkin Methods for the Generalized Korteweg-de Vries
Equation", Math. Comp., Vol. 82(283), July 2013, pp. 1401--1432.
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A. Aristotelous, O. Karakashian, and S.M. Wise, A Mixed Discontinuous
Galerkin, Convex Splitting Scheme for a Modified Cahn-Hilliard Equation
and an Efficient Nonlinear Multigrid Solver, Discrete Cont. Dyn Sys.
Ser. B 18 (2013) 2211--2238.
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A. Aristotelous, O. Karakashian, and S.M. Wise, Adaptive, Second-Order in
Time, Primitive-Variable Discontinuous Galerkin Schemes for a
Cahn-Hilliard Equation with a Mass Source Term, IMA J. Numer. Anal. 35
(2015) 1167--1198.
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O. Karakashian and C. Makridakis, ``A posteriori error
estimates for discontinuous-Galerkin Methods for the Generalized
Korteweg-de Vries Equation". Math. Comp. Vol. 84, No. 293, May 2015.
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O. Karakashian and Y. Xing, ``A posteriori error estimates for
conservative Local Discontinuous Galerkin methods for the Generalized
Korteweg-de Vries equation''. Communications in Comp. Phys.,
Vol. 20 (1), 2016, pp. 250--278.
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J. L. Bona, H. Chen and O. Karakashian, ``Stability of solitary-wave
solutions of systems of dispersive equations". Applied
Mathematics and Optimization, 2015, (Electronic).
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O. Karakashian and C. Collins, ``Two-level additive Schwarz methods for
discontinuous Galerkin approximations of second-order elliptic
equations''. IMA Jour. of Numer. Anal. (Electronic).
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O. Karakashian and C. Collins, ``Two-level additive Schwarz methods for
discontinuous Galerkin approximations of the Biharmonic equation''.
To appear in Jour. of Sci. Comput.
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