Georgios Akrivis, Professor Emeritus


Department of Computer Science
and Engineering
University of Ioannina
Ioannina
Greece, GR-45110

Tel: +30-26510-08800
Email: akrivis (at) cse.uoi.gr

Γεώργιος Ακρίβης, Ομότιμος Καθηγητής


Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών
και Πληροφορικής
Πανεπιστήμιο Ιωαννίνων
Ιωάννινα
45110

Τηλ. 26510-08800
Email: akrivis (at) cse.uoi.gr

 

Service to the Profession / Προσφορά στο Επάγγελμα

    • Associate Editor of SIAM Journal on Numerical Analysis (since 2019).
    • Member of the Sectorial Scientific Council (TES) for Mathematics and Information Sciences,
      National Council for Research and Innovation, GSRT, Greece (from April 10, 2018, until October 24, 2019).

Teaching / Διδασκαλία

Curriculum Vitae PDF / Βιογραφικό Σημείωμα PDF

Education / Σπουδές

    B.Sc. University of Ioannina, Greece, 1973
    Ph.D. University of Munich, Germany, 1983
    Πτυχίο Μαθηματικών, Πανεπιστήμιο Ιωαννίνων, 1973
    Διδακτορικό, Πανεπιστήμιο Μονάχου, 1983

Research Interests / Ερευνητικά Ενδιαφέροντα

    Numerical methods for partial differential equations.
    Αριθμητικές μέθοδοι για μερικές διαφορικές εξισώσεις.

Publications / Δημοσιεύσεις

  • G. Akrivis, M. Chen, F. Yu: The weighted and shifted seven-step BDF method for parabolic equations. IMA J. Numer. Anal. (to appear) doi: 10.1093/imanum/drae089 PDF
  • G. Akrivis, S. Bartels, Ch. Palus: Quadratic constraint consistency in the projection-free approximation of harmonic maps and bending isometries. Math. Comp. (to appear) doi: 10.1090/mcom/4035 PDF
  • G. Akrivis, B. Li, R. Tang, H. Zhang: High-order mass-, energy- and momentum-conserving methods for the nonlinear Schrödinger equation. J. Comp. Phys. 532 (2025) 113974, 21 pp. doi: 10.1016/j.jcp.2025.113974 PDF
  • G. Akrivis, M. Chen, J. Han, F. Yu, Z. Zhang: The variable two-step BDF method for parabolic equations. BIT Numer. Math. 64 (2024), Paper no. 14, 21 pp. doi: 10.1007/s10543-024-01007-y PDF
  • G. Akrivis, Ch. G. Makridakis: A posteriori error estimates for Radau IIA methods via maximal parabolic regularity. Numer. Math. 150 (2022) 691–717. doi: 10.1007/s00211-022-01271-6 PDF
  • G. Akrivis, Ch. G. Makridakis: On maximal regularity estimates for discontinuous Galerkin time-discrete methods. SIAM J. Numer. Anal. 60 (2022) 180–194. PDF
  • G. Akrivis, B. Li: Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation. IMA J. Numer. Anal. 42 (2022) 363–391. PDF
  • G. Akrivis, M. Chen, F. Yu, Z. Zhou: The energy technique for the six-step BDF method. SIAM J. Numer. Anal. 59 (2021) 2449–2472. PDF
  • G. Akrivis, B. Li: Linearization of the finite element method for gradient flows by Newton’s method. IMA J. Numer. Anal. 41 (2021) 1411–1440. PDF
  • G. Akrivis, D. Li: Structure-preserving Gauss methods for the nonlinear Schrödinger equation. Calcolo 58 (2021), Paper no. 17, 25 pp. PDF
  • G. Akrivis, M. Feischl, B. Kovács, Ch. Lubich: Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. Math. Comp. 90 (2021) 995–1038. PDF
  • G. Akrivis, B. Li, J. Wang: Convergence of a second-order energy-decaying method for the viscous rotating shallow water equation. SIAM J. Numer. Anal. 59 (2021) 265–288. PDF
  • G. Akrivis, E. Katsoprinakis: An analogue to the A(θ)-stability concept for implicit–explicit BDF methods. SIAM J. Numer. Anal. 58 (2020) 3475–3503. PDF
  • G. Akrivis, E. H. Georgoulis: Implicit–explicit multistep methods for nonlinear convection–diffusion equations. In: Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018, ed. by G. R. Barrenechea, J. Mackenzie, Lecture Notes in Computational Science and Engineering v. 135, Springer, 2020, pp. 59–81. PDF
  • G. Akrivis, E. Katsoprinakis: Maximum angles of A(θ)-stability of backward difference formulae. BIT Numer. Math. 60 (2020) 93–99. PDF
  • G. Akrivis, B. Li, D. Li: Energy-decaying extrapolated RK-SAV methods for the Allen–Cahn and Cahn–Hilliard equations. SIAM J. Scientific Computing 41 (2019) A3703–A3727. PDF
  • G. Akrivis: Stability of implicit and implicit–explicit multistep methods for nonlinear parabolic equations. IMA J. Numer. Anal. 38 (2018) 1768–1796. PDF
  • G. Akrivis, B. Li: Maximum norm analysis of implicit–explicit backward difference formulae for nonlinear parabolic equations. IMA J. Numer. Anal. 38 (2018) 75–101. PDF
  • G. Akrivis, B. Li, Ch. Lubich: Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations. Math. Comp. 86 (2017) 1527–1552. PDF
  • G. Akrivis, Y.–S. Smyrlis: Backward difference formulae for Kuramoto–Sivashinsky type equations. Calcolo 54 (2017) 685–709. PDF
  • G. Akrivis: Stability properties of implicit–explicit multistep methods for a class of nonlinear parabolic equations. Math. Comp. 85 (2016) 2217–2229. PDF
  • G. Akrivis, E. Katsoprinakis: Backward difference formulae: new multipliers and stability properties for parabolic equations. Math. Comp. 85 (2016) 2195–2216. PDF
  • G. Akrivis, A. Kalogirou, D. T. Papageorgiou, Y. S. Smyrlis: Linearly implicit schemes for multi-dimensional Kuramoto-Sivashinsky type equations arising in falling film flows. IMA J. Numer. Anal. 36 (2016) 317–336. PDF
  • G. Akrivis: Stability of implicit–explicit backward difference formulas for nonlinear parabolic equations. SIAM J. Numer. Anal. 53 (2015) 464–484. PDF
  • G. Akrivis, Ch. Lubich: Fully implicit, linearly implicit and implicit–explicit backward difference formulae for quasi-linear parabolic equations. Numer. Math. 131 (2015) 713–735. PDF
  • G. Akrivis, D. T. Papageorgiou, Y. S. Smyrlis: On the analyticity of certain dispersive-dissipative systems. Bull. London Math. Soc. 45 (2013) 52–60. PDF
  • G. Akrivis: Implicit–explicit multistep methods for nonlinear parabolic equations. Math. Comp. 82 (2013) 45–68. PDF
  • G. Akrivis, D. T. Papageorgiou, Y. S. Smyrlis: Computational study of the dispersively modified Kuramoto–Sivashinsky equation. SIAM J. Scientific Computing 34 (2012) A792–A813. PDF
  • G. Akrivis, Ch. Makridakis, R. H. Nochetto: Galerkin and Runge-Kutta methods: Unified formulation, a posteriori error estimates and nodal superconvergence. Numer. Math. 118 (2011) 429–456. PDF
  • G. Akrivis, Y. S. Smyrlis: Linearly implicit schemes for a class of dispersive–dissipative systems. Calcolo 48 (2011) 145–172. PDF
  • G. Akrivis, D. T. Papageorgiou, Y. S. Smyrlis: Linearly implicit methods for a semilinear parabolic system arising in two-phase flows. IMA J. Numer. Anal. 31 (2011) 299–321. PDF
  • G. Akrivis, P. Chatzipantelidis: A posteriori error estimates for the two-step backward differentiation formula method for parabolic equations. SIAM J. Numer. Anal. 48 (2010) 109–132. PDF
  • G. Akrivis, Ch. Makridakis, R. H. Nochetto: Optimal order a posteriori error estimates for a class of Runge–Kutta and Galerkin methods. Numer. Math. 114 (2009) 133–160. PDF
  • G. Akrivis, Ch. Makridakis, R. H. Nochetto: A posteriori error estimates for the Crank–Nicolson method for parabolic equations. Math. Comp. 75 (2006) 511–531. PDF
  • G. Akrivis, S. Larsson: Linearly implicit finite element methods for the time-dependent Joule heating problem. BIT Numer. Math. 45 (2005) 429–442. PDF
  • G. Akrivis, Y. S. Smyrlis: Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation. Appl. Numer. Math. 51 (2004) 151-169. PDF
  • G. Akrivis, Ch. Makridakis: Galerkin time-stepping methods for nonlinear parabolic equations. Math. Mod. Numer. Anal. 38 (2004) 261–289. PDF
  • G. Akrivis, M. Crouzeix: Linearly implicit methods for nonlinear parabolic equations. Math. Comp. 73 (2004) 613–635. PDF
  • G. Akrivis, F. Karakatsani: Modified BDF methods for nonlinear parabolic equations. BIT Numer. Math. 43 (2003) 467–483. PDF
  • G. Akrivis, O. Karakashian, F. Karakatsani: Linearly implicit methods for nonlinear evolution equations. Numer. Math. 94 (2003) 403–418. PDF
  • G.D. Akrivis, V.A. Dougalis, O.A. Karakashian, W.R. McKinney: Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrödinger equation. SIAM J. Scientific Computing 25 (2003) 186–212. PDF
  • G.D. Akrivis, V.A. Dougalis, G. E. Zouraris: Finite difference schemes for the `parabolic' equation in a variable depth environment with a rigid bottom boundary condition. SIAM J. Numer. Anal. 39 (2001) 539–565. PDF
  • G. Akrivis, M. Crouzeix, Ch. Makridakis: Implicit–explicit multistep methods for quasilinear parabolic equations. Numer. Math. 82 (1999) 521–541. PDF
  • G. Akrivis: Finite difference methods for a wide-angle "parabolic" equation. SIAM J. Numer. Anal. 36 (1999) 317–329. PDF
  • G. Akrivis, M. Crouzeix, Ch. Makridakis: Implicit-explicit multistep finite element methods for nonlinear parabolic problems. Math. Comp. 68 (1998) 457–477. PDF
  • G. Akrivis, V. A. Dougalis, O. Karakashian: Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods. Math. Mod. Numer. Anal. 31 (1997) 251–287. PDF
  • G. D. Akrivis, V. A. Dougalis, G. E. Zouraris: Error estimates for finite difference methods for the wide–angle "parabolic" equation. SIAM J. Numer. Anal. 33 (1996) 2488–2509. PDF
  • G. Akrivis: High-order finite element methods for the Kuramoto-Sivashinsky equation. Math. Mod. Numer. Anal. 30 (1996) 157–183. PDF
  • G. Akrivis, M. Crouzeix, V. Thomee: Numerical methods for ultraparabolic equations. Calcolo 31 (1994) 179–190. PDF
  • G. D. Akrivis, V. A. Dougalis, N. A. Kampanis: Error estimates for finite element methods for a wide–angle parabolic equation. Appl. Numer. Math. 16 (1994) 81–100. PDF
  • G. D. Akrivis, V. A. Dougalis, N. A. Kampanis: On Galerkin methods for the wide–angle parabolic equation. Journal of Computational Acoustics 2 (1994) 99–112. PDF
  • O. Karakashian, G. Akrivis, V. A. Dougalis: On optimal-order error estimates for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 30 (1993) 377–400. PDF
  • G. Akrivis: Finite difference discretization of the cubic Schrödinger equation. IMA J. Numer. Anal. 13 (1993) 115–124. PDF
  • G. Akrivis: Finite difference discretization of the Kuramoto-Sivashinsky equation. Numer. Math. 63 (1992) 1–11. PDF
  • G. Akrivis, V. A. Dougalis, O. Karakashian: On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation. Numer. Math. 59 (1991) 31–53. PDF
  • G. Akrivis, V. A. Dougalis: Finite difference discretizations of some initial and boundary value problems with interface. Math. Comp. 56 (1991) 505–522. PDF
  • G. Akrivis, V. A. Dougalis: On a class of conservative, highly accurate Galerkin methods for the Schrödinger equation. (RAIRO:) Math. Model. and Numer. Anal. 25 (1991) 643–670. PDF
  • G. Akrivis, V. A. Dougalis: Finite difference discretization with variable mesh of the Schrödinger equation in a variable domain. Bull. Greek Mathem. Soc. 31 (1990) 19–28. PDF

Books (in Greek) / Βιβλία

  • G. D. Akrivis, V. A. Dougalis: Introduction to Numerical Analysis. Crete University Press, Heraklion, 1997 (fifth edition: 2021).
    Γ. Δ. Ακρίβης, Β. Α. Δουγαλής: Εισαγωγή στην Αριθμητική Ανάλυση. Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 1997 (πέμπτη έκδοση: 2021).
  • G. D. Akrivis, V. A. Dougalis: Numerical Methods for Ordinary Differential Equations. Crete University Press, Heraklion, 2006. (second edition: 2013, second printing: 2018).
    Γ. Δ. Ακρίβης, Β. Α. Δουγαλής: Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 2006 (δεύτερη έκδοση: 2013, δεύτερη ανατύπωση: 2018).
  • G. D. Akrivis, N. D. Alikakos: Partial Differential Equations. Synchroni Ekdotiki, Athens, 2012 (second edition: 2017).
    Γ. Δ. Ακρίβης, Ν. Δ. Αλικάκος: Μερικές Διαφορικές Εξισώσεις. Σύγχρονη Εκδοτική, Αθήνα, 2012 (δεύτερη έκδοση: 2017).