1. 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.
    Download PDF

  2. 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.
    Download PDF

  3. 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.
    Download PDF

  4. 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.
    Download PDF

  5. 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.
    Download PDF

  6. 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.
    Download PDF

  7. 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.
    Download PDF

  8. O. Karakashian, ``On Runge-Kutta methods for parabolic problems with time-dependent coefficients'', Math. Comp., Vol. 47, No. 175, 1986, pp. 77-101.
    Download PDF

  9. 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.
    Download PDF

  10. 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.
    Download PDF

  11. 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.
    Download PDF

  12. 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.
    Download PDF

  13. 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.
    Download PDF

  14. 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.
    Download PDF

  15. 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.
    Download PDF

  16. 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.

  17. 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.
    Download PDF

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 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.
    Download PDF

  23. 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.

  24. 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.
    Download PDF

  25. 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.

  26. 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.

  27. 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.

  28. 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.
    Download PDF

  29. 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.
    Download PDF

  30. 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.

  31. 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.
    Download PDF

  32. 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.

  33. 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.
    Download PDF

  34. 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.

  35. 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.

  36. G. Akrivis, O. Karakashian and F. Karakatsani,``Linearly implicit methods for nonlinear evolution equations'', Numer. Mathematik, Vol. 94, No. 3, 2003, pp. 403--418.
    Download PDF

  37. 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.
    Download PDF

  38. 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.
    Download PDF

  39. 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.
    Download PDF

  40. 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.
    Download PDF

  41. 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.
    Download PDF

  42. 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.
    Download PDF

  43. 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.
    Download PDF

  44. 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.
    Download PDF

  45. 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.

  46. 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.
    Download PDF

  47. 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.
    Download PDF

  48. 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.
    Download PDF

  49. 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.
    Download PDF

  50. 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.
    Download PDF

  51. J. L. Bona, H. Chen and O. Karakashian, ``Stability of solitary-wave solutions of systems of dispersive equations". Applied Mathematics and Optimization, 2015, (Electronic).
    Download PDF

  52. 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).
    Download PDF

  53. 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.
    Download PDF