SCIENTIFIC COMPUTING & SOFTWARE DEVELOPMENT

Scientific Computing & Software Development

ABOUT R&D ACTIVITIES R&D PROGRAMS PUBLICATIONS PEOPLE CONTACT US

ABOUT

IACM’s long tradition in Numerical Analysis and Scientific Computing research is focused on both fundamental research as well as on applied, industrial applications. Our aim is the development, implementation, evaluation and analysis of numerical methods for the accurate and efficient simulation of challenging continuum and stochastic mathematical models. Our expertise spans on a variety of computational methods and alternative methodologies. Specific applications the team is actively involved with are: computational fluid dynamics, numerical simulation of crack propagation, methods for conservation laws, dispersive wave propagation, viscous flow through heterogeneous media, large scale convective flows, and drift-diffusion systems with applications in solar cells, to name a few.

A considerable effort will be made to pitch as many as current fundamental research projects as possible into potentially interested industrial partners in Greece and abroad, aiming to expand their applicability and to facilitate their transition from enquiry-driven research into technological innovation.

RESEARCH AND DEVELOPMENT ACTIVITIES

Scientific Computing: We develop algorithms and software for the numerical modelling of complex systems and phenomena. Specific applications group members are actively involved with are: computational fluid dynamics, numerical simulation of crack propagation, methods for conservation laws, dispersive wave propagation, viscous flow through heterogeneous media.

Some recent activities:

Development of space-time adaptive algorithms for capturing singular phenomena such as: shocks, shear bands, localized solutions of nonlinear evolutionary PDEs. The development of next-generation space-time adaptive algorithms for the numerical approximation of solutions of nonlinear PDEs exhibiting singular behavior. Although adaptive algorithms are increasingly becoming a sought-after computational complexity reduction device in industrial, large scale simulators in various disciplines (aeronautics, material science, structural dynamics, geosciences), their mathematical foundations are still largely unexplored in the more challenging contexts of locally singular phenomena.
The development and study of novel, rigorous, structure-preserving numerical methods for the accurate and efficient simulation of challenging kinetic equations with highly complex collision kernels, following exciting recent paradigm-shift developments in the mathematical analysis of such kinetic models. Moreover, notwithstanding the important fundamental research implications, the development of new high-order, structure-preserving numerical simulation capabilities for Boltzmann, Landau or Vlasov-type equations is deemed to enhance the potential of collaboration between IACM and other institutes’ research directions, especially in the context of statistical physics.
The development of novel multiscale numerical methods for flows through heterogeneous materials with specific applications arising in geo-engineering and oil-reservoir/petroleum modelling. The recent development of numerical methods on general polytopic cells/elements (by IACM members), in conjunction with respective modern numerical upscaling techniques has the potential of achieving unprecedented computational complexity reduction in realistic geological porous media flow scenarios.
We have considerable expertise on coupling models across scales. Multiscale models are devised utilising solid numerical analysis methodologies and satisfy certain structure-preserving criteria. The reliability of the approaches taken are checked using mathematical analysis tools. Key applications include atomistic-continuum coupling in the modelling of crack propagation in materials as well as kinetic-continuum coupled models.
Rigorous theory for a variety of numerical methods, including a posteriori error bounds for time-dependent problems, fundamental questions for time stepping schemes, analysis of approximation for dispersive problems, finite volume and virtual element methods, positivity preserving schemes, error analysis for PDE control problems.
The development of a general framework for numerical methods on polygonal and polyhedral elements with arbitrary shapes and number of faces based on discontinuous Galerkin approaches, paving the way for next generation computational model reduction approaches.
Novel methods for energy minimisation problems, including appropriate discontinuous Galerkin formulations, convergence analysis towards minimisers, stabilisation mechanisms as solution selection criteria.

Education and Training: The group contributes to the education and training of undergraduate, graduate and post-graduate students as well as of PhD candidates and Postdoctoral researchers.

Scientific Computing & Software Development

RESEARCH AND DEVELOPMENT PROGRAMS

A. ONGOING PROJECTS

Title: Modeling Transcription: an integrated approach to understand cancer-specific gene expression programs
Funding Source: Hellenic Foundation for Research and Innovation (H.F.R.I.)
Duration: 2023-2025

B. COMPLETED PROJECTS

Title: «Ανισοτροπική Αναπροσαρμογή στην Προτυποποίηση με Πεπερασμένα Στοιχεία»
Funding Source and funding scheme: Hellenic Foundation for Research and Innovation (H.F.R.I.), 1st Call for H.F.R.I. Research Projects to Support Faculty Members & Researchers and Procure High-Value Research Equipment
Duration: 2020-2023
Title: Machine Learning, Statistical Modelling and Uncertainty Quantification for PV Performance Output Prediction
Funding Source: Saudi ARAMCO Saudi Arabia, IACM-FORTH
Duration: 2020-2022
Title: ETAK: Research and development of engineering software tools for the application of contemporary strengthening methods for existing building,
Funding Source: ΕΣΠΑ, Program: Operational Programme “Competitiveness, Enterpreneurship and Innovation”
Duration: 2018-2022

PUBLICATIONS

2024
- A Athanassoulis, T Katsaounis, I Kyza (2024) Efficient numerical approximations for a non-conservative Nonlinear Schrodinger equation appearing in wind-forced ocean waves, arXiv preprint arXiv:2401.16835
- GR Barrenechea, EH Georgoulis, T Pryer, A Veeser (2024) A nodally bound-preserving finite element method, IMA Journal of Numerical Analysis 44 (4), 2198-2219.
- E Casas, K Chrysafinos, M Mateos (2024) Error estimates for the discretization of bilinear control problems governed by semilinear elliptic PDEs, arXiv preprint arXiv:2404.05658
- K Chrysafinos, EH Georgoulis, VD Papadopoulos (2024) Mesh-Dependent L^2-Like Norm a Posteriori Error Estimates for Elliptic Problems with Non-essential Boundary Conditions, Journal of Scientific Computing 100 (1), 8.
- Z Dong, EH Georgoulis, PJ Herbert (2024) A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation, arXiv preprint arXiv:2401.12921
- RE Fernandes, EH Georgoulis, A Paganini (2024) Level-set shape optimization via polytopic discontinuous Galerkin methods, arXiv preprint arXiv:2408.13206
- E Georgoulis, A Papapantoleon, C Smaragdakis (2024) A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models, arXiv preprint arXiv:2401.06740
- G Grekas, CG Makridakis (2024) Deep Ritz-Finite Element methods: Neural Network Methods trained with Finite Elements, arXiv preprint arXiv:2409.08362
- C Kalaitzidou, G Grekas, A Zilian, C Makridakis, P Rosakis (2024) Compressive instabilities enable cell-induced extreme densification patterns in the fibrous extracellular matrix: Discrete model predictions, PLOS Computational Biology 20 (7), e1012238 (pdf file)
- Y Kamarianakis, Y Pantazis, E Kalligiannaki, TD Katsaounis, K Kotsovos, I Gereige, M Abdullah, A Jamal, A Tzavaras (2024) Robust day-ahead solar forecasting with endogenous data and sliding windows, J. Renewable Sustainable Energy 16 (026103), 1-13.
- T Katsaounis, I Mousikou, AE Tzavaras (2023) Axisymmetric flows with swirl for Euler and Navier-Stokes equations, Journal of Nonlinear Science, Vol. 34(5), 86. https://doi.org/10.1007/s00332-024-10064-0
- DA Mitsoudis, M Plexousakis, GN Makrakis, C Makridakis (2024) Approximations of the Helmholtz equation with variable wave number in one dimension, Studies in Applied Mathematics, e12756 (pdf file)
2023
- A. Athanassoulis, T. Katsaounis, I. Kyza, S. Metcalfe (2023) A novel, structure-preserving, second-order-in-time relaxation scheme for Schrodinger-Poisson systems, Journal of Computational Physics(JCP) [1], vol. 490, 112307, https://doi.org/10.1016/j.jcp.2023.112307
- G Barrenechea, E Georgoulis, T Pryer, A Veeser (2023) A nodally bound-preserving finite element method, arXiv preprint arXiv:2304.01067
- A Cangiani, Z Dong, EH Georgoulis (2023) A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes, SIAM Journal on Numerical Analysis 61 (5), 2352-2380.
- Casas E., Chrysafinos K., Mateos M., (2023) Bilinear control of semilinear elliptic PDEs: Convergence of a semismooth Newton method, arXiv:2309.07554
- E Casas, K Chrysafinos, M Mateos (2023) Semismooth Newton Method for Boundary Bilinear Control, IEEE Control Systems Letters
- E Casas Rentería, K Chrysafinos, M Mateos Alberdi (2023) Semismooth newton method for boundary bilinear control, Institute of Electrical and Electronics Engineers, Inc.
- Chrysafinos K., Plaka D., (2023) Analysis and approximations of an optimal control problem for the Allen–Cahn equation, Numerische Mathematik, 155, pp. 35–82.
- Dougalis, V.A., Duran, A. and Saridaki, L. (2023) On the numerical approximation of Boussinesq / Boussinesq systems for internal waves, Numerical Methods for Partial Differential Equations, https://doi.org/10.1002/num.23021
- A Cangiani, Z Dong, EH Georgoulis (2023) A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes, SIAM Journal on Numerical Analysis 61 (5), 2352-2380
- Gazoulis D., Gkanis I., Makridakis C.G., (2023) On the Stability and Convergence of Physics Informed Neural Networks, arXiv:2308.05423
- Georgoulis E.H., Loulakis M., Tsiourvas A., (2023) Discrete gradient flow approximations of high dimensional evolution partial differential equations via deep neural networks, Communications in Nonlinear Science and Numerical Simulation, Vol. 117, Feb. 2023, 106893. (html file)
- Georgoulis E.H., Makridakis C.G., (2023) Lower bounds, elliptic reconstruction and a posteriori error control of parabolic problems, IMA Journal of Numerical Analysis 43 (6), 3212-3242, https://doi.org/10.1093/imanum/drac080
- Grekas G., Koumatos K., Makridakis C., Vikelis A., (2023) A class of Discontinuous Galerkin methods for nonlinear variational problems, arXiv preprint arXiv:2308.12891
- Loulakis M., Makridakis C.G., (2023) A new approach to generalisation error of machine learning algorithms: Estimates and convergence, arXiv preprint, arXiv:2306.13784
2022
- Akrivis, G., Li, B., (2022) ‘Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation’. IMA J. Numer. Anal. 42 (2022) 363–391.
- Akrivis, G., Makridakis, C. (2022) On maximal regularity estimates for discontinuous Galerkin time-discrete methods, SIAM J. Numer. Anal., 60(1), 180–194.
- Akrivis, G., Makridakis, Ch. ‘A posteriori error estimates for Radau IIA methods via maximal parabolic regularity’. Numerische Mathematik 150 (3), 691-717.
- Alsheikh, D.N., Katsaounis, T., (2022) A posteriori error estimators for discontinuous Galerkin method for diffusion problems, based on the hypercircle method, Arabian Journal of Mathematics, 11 (3), pp. 407-426. https://doi.org/10.1007/s40065-022-00386-w
- Banjai L. and Makridakis, CG. 'A posteriori error analysis for approximations of time-fractional subdiffusion problems', Mathematics of Computation, accepted, 91 (336), 1711-1737, DOI: https://doi.org/10.1090/mcom/3723
- Cangiani, A., Dong, Z., Georgoulis, E.H. (2022). hp–Version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. Mathematics of Computation 91 pp. 1-35.
- Z Dong, EH Georgoulis (2022) Robust interior penalty discontinuous Galerkin methods, Journal of Scientific Computing 92 (2), 57.
- Dougalis, V.A., Duran, A. and Saridaki, L. (2022) Numerical solution of internal-wave systems in the Intermediate Long Wave and Benjamin-Ono regimes, Bulletin of the Hellenic Mathematical Society, Vol. 66, pp. 11-25.
- Grekas, G., Koumatos, K., Makridakis, C., Rosakis, P., Approximations of energy minimization in cell-induced phase transitions of fibrous biomaterials: -convergence analysis, arXiv preprint arXiv:1907.01382. Accepted in SIAM Journal on Numerical Analysis.
- Israwi, S., Kalisch, H., Katsaounis, T., Mitsotakis, D., (2022) A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis (2022) Nonlinearity, 35 (1), pp. 750-786. https://doi.org/10.1088/1361-6544/ac3c29
- T Katsaounis, G Kounadis, I Mousikou, AE Tzavaras (2022) Optimization Methods for One Dimensional Elastodynamics, arXiv preprint arXiv:2208.13657
- T Katsaounis, I Mousikou, AE Tzavaras (2022) Self-similar axisymmetric flows with swirl, XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications, pp. 407-417.
2021
- Akrivis, G., Chen, M., Yu, F., Zhou, Z., (2021) ’The energy technique for the six-step BDF method’. SIAM J. Numer. Anal. 59 (2021) 2449–2472.
- Akrivis, G., Feischl, M., Kovács, B., Lubich, Ch. (2021) ‘Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation’. Math. Comp. 90 (2021) 995–1038.
- Akrivis, G., Li, B. (2021) ‘Linearization of the finite element method for gradient flows by Newton’s method’, IMA J. Numer. Anal. 41 (2021) 1411–1440.
- Akrivis, G., Li, B., Wang, J., (2021) ‘Convergence of a second-order energy-decaying method for the viscous rotating shallow water equation’. SIAM J. Numer. Anal. 59 (2021) 265–288.
- Akrivis, G., Li, D., (2021) ‘Structure-preserving Gauss methods for the nonlinear Schrödinger equation’. Calcolo 58 (2021), Paper no. 17, 25 pp.
- Cangiani, A., Georgoulis, E.H., Sutton, O.J. (2021) Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods. Mathematical Models and Methods in Applied Sciences 31(4) pp. 711-751.
- Dong, Z., Georgoulis, E.H., Kappas, T. (2021) GPU-accelerated discontinuous Galerkin methods on polytopic meshes. SIAM Journal on Scientific Computing 43(4) pp. C312–C334.
- Dougalis, V.A.,Duran, A., and Saridaki, L. (2021) On solitary-wave solutions of Boussinesq / Boussinesq systems for internal waves, Physica D: Nonlinear Phenomena, Vol. 428, https://doi.org/10.1016/j.physd.2021.133051
- Georgoulis, E.H. (2021) Hypocoercivity-compatible finite element methods for the long-time computation of Kolmogorov's equation. SIAM Journal on Numerical Analysis 59(1) pp.173-194.
- Georgoulis, E.H., Lakkis, O., Wihler, T.P. (2021) A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems. Numerische Mathematik 148(2) pp.363–386 (2021).
- Gkanis, I., Makridakis, C., (2021) A new class of entropy stable schemes for hyperbolic systems: Finite element methods, Math. Comp. 90 (2021), 1663-1699.
- Kounadis, G., Antonopoulos, D.C. and Dougalis, V.A. (2021) ‘Galerkin finite element methods for the numerical solution of two classical-Boussinesq type systems over variable bottom’, Wave Motion v.102, 102715.
2020
- Akrivis, G., Georgoulis, EH (2020) ‘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.
- Akrivis, G., Katsoprinakis, E., (2020) ‘Maximum angles of A(θ)-stability of backward difference formulae’. BIT Numer. Math. 60 (2020) 93–99.
- Akrivis, G., Katsoprinakis, E., (2020), An analogue to the A(θ)-stability concept for implicit–explicit BDF methods’. SIAM J. Numer. Anal. 58 (2020) 3475–3503.
- Antonopoulos, D.C., Dougalis, V.A. and Kounadis, G. (2020) ‘On the standard Galerkin method with explicit RK4 time stepping for the Shallow Water equations’, IMA J.Numer.Anal. v.40, 2415-2449; also arXiv: 1810.11008.
- Cangiani, A., Chatzipandelidis, P., Diwan, G., Georgoulis, E.H. (2020) A virtual element method for quasilinear elliptic problems. IMA Journal of Numerical Analysis 40 (4), pp.2450--2472.
- Cangiani, A., Georgoulis, E.H., Sabawi, M. (2020) A posteriori error analysis for implicit–explicit hp-discontinuous Galerkin timestepping methods for semilinear parabolic problems. Journal of Scientific Computing 82(2), Paper No. 26, 24 pp.
- Cangiani, A., Georgoulis, E.H., Sabawi, Y. (2020) Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems. Journal of Computational and Applied Mathematics 367, 112397, 15.
- Dong, Z., Georgoulis, E.H., Pryer, T. (2020) Recovered Finite Element Methods on polygonal and polyhedral meshes. ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 4, pp.1309–1337.
- Gkanis, I., Grekas, G., Karnessis, E., Makridakis, C., Mathematics of computational modelling: some challenges of computing nonlinear phenomena in First Congress of Greek Mathematicians, Pages: 139–166, De Gruyter, 2020.
- Katsaounis, T., Kotsovos, K., Gereige, I., Basaheeh, A., Abdullah, M., Khayat, A., Al-Habshi, E., Al-Saggaf, A. and A. Tzavaras, A. (2020) Seasonal Performance Assesment of Various PV Technologies in a Desert Climate Through Device Simulations and Outdoor Measurements, Proceeding of 37th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC2020), pp.1112 – 1116.
- Katsaounis, T., Mitsotakis, D., Sadaka, G., (2020) Boussinesq-Peregrine water wave models and their numerical approximation, Journal of Computational Physics, vol.417, 109579.
- Kounadis, G. and Dougalis, V.A., (2020) `Galerkin finite element methods for the shallow water equations over variable bottom’, J. Computational and Applied Mathematics v.373, 112315; also arXiv: 1901.04230.
2019
- Akrivis, G., Li, B., Li, D., (2019) ‘Energy-decaying extrapolated RK-SAV methods for the Allen–Cahn and Cahn–Hilliard equations’. SIAM J. Scientific Computing 41 (2019) A3703–A3727.
- D Antonopoulou, M Plexousakis (2019) A posteriori analysis for space-time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain, ESAIM: Mathematical Modelling and Numerical Analysis 53 (2), 523-549.
- Cangiani, A., Georgoulis, E.H., Giani, S., Metcalfe, S. (2019) hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. Computers and Mathematics with Applications no. 9, pp. 3090–3104.
- Casas, E., Chrysafinos, K. (2019) “Numerical analysis of quasilinear parabolic equations under low regularity assumptions”, Numer. Math., (143), pp 749-780 https://doi.org/10.1007/s00211-019-01071-5
- Chrysafinos, K., (2019) “Stability analysis and best approximation error estimates of discontinuous time stepping schemes for the Allen-Cahn equation”, ESAIM: M2AN, (53), pp 551-583 https://doi.org/10.1051/m2an/2018071
- Chrysafinos, K., Karatzas, E., Kostas, D. (2019) “Stability and error estimates of fully discrete schemes for the Brusselator system”, SIAM J. Numer. Anal. (57), pp 828-853. https://doi.org/10.1137/18M1185594
- Georgoulis, E.H., Hall, E. and Makridakis, C. (2019) An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems. IMA Journal of Numerical Analysis 39(1) pp. 34--60.
- Katsaounis, T., Kotsovos, K., Gereige, I., Basaheeh, A., Abdullah, M., Khayat, A., Al-Habshi, E., Al-Saggaf, A. and Tzavaras, A. (2019) Performance assessment of bifacial c-Si PV modules through device simulations and outdoor measurements, Renewable Energy, vol.143, pp. 1285-1298.
- Katsaounis, T. with K. Kotsovos, I. Gereige, A. Basaheeh, M. Abdullah, A. Khayat, E. Al-Habshi, A. Al-Saggaf, and A. Tzavaras, (2019) Performance Assessment of various PV module types under desert conditions through device simulations and outdoor measurements, Proceeding of 36th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC2019), pp.874-879, 2019.
- Lee, M-G., Katsaounis, T. and Tzavaras, A., (2019) Localization in adiabatic shear flow via geometric theory of singular perturbations, Journal of Nonlinear Science, 29, 2055-2101.
- Rekatsinas, N., Stevenson R., (2019) 'An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems' Advances in Computational Mathematics 45 (2), 1031-1066 https://link.springer.com/article/10.1007/s10444-018-9644-2
2018
- Akrivis, G., (2018) ‘Stability of implicit and implicit–explicit multistep methods for nonlinear parabolic equations’. IMA J. Numer. Anal. 38 (2018) 1768–1796.
- Akrivis, G., Li, B., (2018) ‘Maximum norm analysis of implicit–explicit backward difference formulae for nonlinear parabolic equations. IMA J. Numer. Anal. 38 (2018) 75–101.
- Bansch, E., Karakatsani, F., Makridakis, C., (2018) A posteriori error estimates for fully discrete schemes for the time dependent Stokes problem. no. 2, Paper No. 19, Calcolo 55, No. 19, 32 pp.
- Cangiani, A., Georgoulis, E.H. and Sabawi, Y. (2018) Adaptive discontinuous Galerkin methods for elliptic interface problems. Mathematics of Computation 87(314) pp. 2675 – 2707.
- Cangiani, A., Georgoulis, E.H., Morozov, A. Yu., and Sutton, O.J. (2018) Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework. Proceedings of the Royal Society A 474(2213)
- Casas, E., Chrysafinos, K., (2018) “Analysis and optimal control of some quasilinear parabolic equations”, Math. Contr. and Rel. Fields, (8), pp 807-823. http://dx.doi.org/10.3934/mcrf.2018025
- Dong, Z., Georgoulis, E.H., Levesley, J. and Usta, F. (2018) A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients. Computers and Mathematics with Applications 76 pp. 1950 – 1965.
- Flouri, E.T., Dougalis, V.A. and Synolakis, C.E. (2018) ‘Numerical modeling of tsunamis and tsunami vulnerability analysis for Heraklion, Crete’, Mathematical Methods in the Applied Sciences, 41 1068–1073.
- Georgoulis, E.H. and Pryer, T. (2018). Recovered Finite Element Methods. Computer Methods in Applied Mechanics and Engineering 332, pp. 303 – 324.
- Katsaounis, T., Kyza, I., (2018) A posteriori error analysis for evolution nonlinear Schrödinger equations up to the critical exponent, SIAM J. Numerical Analysis (SINUM), vol.56, no.3, pp.1405-1434.
- Katsaounis, T., Mitsotakis, D. (2018) On the reflection of solitons of the nonlinear Schrödinger equation, Mathematical Methods in the Applied Sciences, vol.41, no.3, pp.1013-1018.
- Kreuzer, C. and Georgoulis, E.H. (2018) Convergence of adaptive discontinuous Galerkin methods. Mathematics of Computation 87(314) pp. 2611 – 2640.
- Lee, M-G, Katsaounis, T, Tzavaras A., (2018) Localization of Adiabatic Deformations in Thermoviscoplastic Materials, Proceedings HYP2016: Theory, Numerics and Applications of Hyperbolic Problems II, pp.269-280, Springer, 2018.
- Makridakis, C., (2018) On the Babuska-Osborn approach to finite element analysis: L2 estimates for unstructured meshes. Numerische Mathematik 139, 831–844.
- Rekatsinas, N., Stevenson R., (2018) 'A quadratic finite element wavelet Riesz basis' International Journal of Wavelets, Multiresolution and Information Processing https://doi.org/10.1142/S0219691318500339
- Rekatsinas, N., Stevenson R., (2018) 'An optimal adaptive wavelet method for first order system least squares' Numerische mathematik 140 (1), 191-237 https://link.springer.com/article/10.1007/s00211-018-0961-7
2017
- Antonopoulos, D.C; Dougalis, V.A (2017) Galerkin-finite element methods for the Shallow Water equations with characteristic boundary conditions, IMA J. of Numerical Analysis, v.37,pp. 266-295. (Extended version in arXiv: 1507.08209.)
- Antonopoulos, D.C; Dougalis, V.A; Mitsotakis, D. (2017) Error estimates for Galerkin approximations of the Serre equations, SIAM J.Numer. Anal., v.55, pp.841-868, also arXiv : 1701.00668.
- Banjai, L.; Georgoulis, E. H. and Lijoka O. (2017) A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation. SIAM Journal on Numerical Analysis 55(1), pp.63–86.
- Cangiani, A. Dong, Z. and Georgoulis E. H. (2017) hp–Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM Journal on Scientific Computing 39(4) pp.A1251–A1279
- Cangiani, A.; Dong, Z.; Georgoulis E. H. and Houston P. (2017) hp–Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Springer Briefs in Mathematics.
- Cangiani, A.; Georgoulis, E. H.; Pryer T. and Sutton O. J. (2017) A posteriori error estimates for the virtual element method. Numerische Mathematik 137(4) pp. 857-893.
- Chrysafinos, K.; Hou, L.S. (2017) Semi-discrete error estimates of the evolutionary Stokes equations with inhomogeneous Dirichlet boundary data, Comput. Math. Appl., (73) 2017, pp 1684-1696.
- Chrysafinos, K.; Hou, L.S. (2017) Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation ESAIM M2AN.,(51) 2017, 1501-1526.
- Chrysafinos, K.; Casas, E. (2017) Error estimates for the approximation of the velocity tracking problem with bang-bang controls, ESAIM CoCV, (23) 2017, 1267-291.
- Georgoulis E. H. and Pryer T. (2017) Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data. Calcolo 54(4), pp. 1533-1551.
- Katsaounis, Th., Kotsovos, K., I. Gereige, Al-Saggaf, A., and Tzavaras, A., (2017). 2D simulation and performance evaluation of bifacial rear local contact c-Si solar cells under variable illumination conditions, Solar Energy, vol.158, no.1, pp. 34-41.
- Katsaounis, Th., Lee, M-G., and Tzavaras, A., (2017). Localization in inelastic rate dependent shearing deformations, Journal of the Mechanics and Physics of Solids (JMPS), vol.98, no.1, pp.106-125.
- Katsaounis, Th., Olivier, J., and Tzavaras, A., (2017). Emergence of coherent localized structures in shear deformations of temperature dependent fluids, Archive for Rational Mechanics and Analysis, vol.224, no.1, pp.173-208.
2016
- Antonopoulos, D.C; Dougalis, V.A (2016) Error estimates for the standard Galerkin-finite element method for the Shallow Water equations, Math. Comp.v.85, pp.1143-1182. (Extended version in arXiv: 1403.5699).
- Athanassoulis, A., Katsaounis, Th., Kyza, I., (2016). Regularized semiclassical limits: linear flows with infinite Lyapunov exponents, Communications in Mathematical Sciences (JCMS), vol. 14, no.7, pp.1821-1858.
- Dougalis, V.A.; Duran, A.; Mitsotakis, D. (2016) Numerical approximation of solitary waves of the Benjamin equation, Math. and Computers in Simulation, v. 127, pp. 56-79, dx.doi.org/10.1016/j.matcom.2012.07.008
- Georgoulis, E. H.; Lakkis, O.; Makridakis, C. and Virtanen J. (2016) A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. SIAM Journal on Numerical Analysis 54(1), pp. 120--136
- Katsaounis, Th., Mitsotakis, D., (2016). On the reflection of solitons of the nonlinear Schrödinger equation, Mathematical Methods in the Applied Sciences, vol.41, no.6.
2015
- Antonopoulou, D.C., Karali, G., Plexousakis, M. and Zouraris, G.E., (2015). Crank-Nicolson finite element discretizations for a two dimensional linear Schroedinger-type equation posed in a noncylindrical domain. Math. Comp. 84, 1571-1598.
- Dougalis, V.A.; Duran, A.; Mitsotakis, D. (2015) Numerical solution of the Benjamin equation, Wave Motion v.52, pp.194-215. (Extended version in arXiv: 1310.2749).
- Flouri, E T.; Dougalis, V. A. and Synolakis, C. E. (2015) Numerical modelling of tsunamis and tsunami vulnerability analysis for Heraklion, Crete, M3ST’15, 4th International Conference on Modern Mathematical Methods in Science and Technology, Kalamata, Greece, August 30-Sept. 1, 2015.
- Giesselmann, J., Makridakis, C. and Pryer, T., (2015). A posteriori analysis of discontinuous galerkin schemes for systems of hyperbolic conservation laws. SIAM Journal on Numerical Analysis, 53 (3). pp. 1280-1303. ISSN 0036-1429.
- Karakashian, O. and Makridakis, C., (2015). A posteriori error estimates for discontinuous Galerkin methods for the generalized Kortewegde Vries equation, Math. Comp. 84, no. 293, 1145-1167.
- Katsaounis, Th., Kyza, I., (2015). Aposteriori error control and adaptivity for Crank-Nicolson finite element approximations for the linear Schrödinger equation, Numerische Mathematik, vol.129, no.1, pp. 55-90.
- Lakkis, O., Makridakis, C. and Pryer, T., (2015). A comparison of duality and energy a posteriori estimates for L∞(0, T;L2(Ω)) in parabolic problems, Math. Comp. 84, no. 294, 1537-1569.
2014
- Antonopoulos, D.C; Dougalis, V.A (2014) Error estimates for finite element methods for the shallow water equations, in the Proceedings of NumAn2014-Sixth Conference on Numerical Analysis, Chania, Greece, Sept 2014, ed. by G.Akrivis et al., pp.13-16.
- Benas, N., Chrysoulakis, N., Christakis, N., Kossioris, G. and Plexousakis, M. (2014). WRF parameterization updates based on recent and long-term satellite observations. Conference Proceedings COMECAP 2014, ISBN-978-960-524-430-9.
- Christakis, N., Katsaounis, Th., Kossioris, G. and Plexousakis, M., (2014). On of the Performance of the WRF Numerical Model over Complex Terrain on a High Performance Computing Cluster, (with), Proceedings of High Performance Computing and Comminications (HPCC), Paris, France.
- Dougalis, V.A.; Flouri, ET; Synolakis, C.E. (2014) Tsunami hazard and inundation for the northern coast of Crete, Proceedings of NumAn2014-Sixth Conference on Numerical Analysis, Chania, Greece, Sept 2014, ed. by G.Akrivis et al., pp. 108-111.
- Georgoulis E. H. and Makridakis C. (2014) On a posteriori error control for the Allen-Cahn problem. Mathematical Methods in the Applied Sciences 37(2) pp. 173-179
- Georgoulis, E. H.; Hall, E. and Makridakis C. (2014). A posteriori error control for discontinuous Galerkin methods for first order hyperbolic problems. In Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations: 2012 John H Barrett Memorial Lectures, Springer (2014).
- Giesselmann, J., Makridakis, C., and Pryer, T., (2014). Energy consistent DG methods for the Navier-Stokes-Korteweg system. Mathematics of Computation, 83 (289). pp. 2071-2099. ISSN 0025-5718.
- Makridakis, C., Mitsoudis, D., and Rosakis, P., (2014). On atomistic-to-continuum couplings without ghost forces in three dimensions, Applied Mathematics Research Express 2014 (1), 87-113. arXiv:1211.7158
2013
- Antonopoulos, D.C; Dougalis, V.A (2013) Error estimates for Galerkin approximations of the ‘classical’ Boussinesq system, Math.Comp. v.82, pp.689-717. (Extended version in arXiv: 1008. 4248).
- Antonopoulou, D.C.; Dougalis, V.A.; Zouraris, G.E. (2013) A finite difference method for the wide-angle ‘parabolic’ equation in a waveguide with downsloping bottom, Num.Meth.PDEs, v.29, pp. 1416-1440.
- Dutykh, D., Katsaounis, Th., Mitsotakis, D., (2013). Finite volume methods for unidirectional dispersive wave models, (with), International Journal for Numerical Methods in Fluids, vol.71, pp.717-736.
- Flouri, E.T. Kalligeris, N. Alexandrakis, G. Kampanis, N. and Synolakis, C.E. (2013) Application of a finite difference computational model to the simulation of earthquake generated tsunamis, Applied Numer. Math., vol. 67, 111–125.
- Georgoulis, E. H.; Lakkis, O. and Makridakis, C. (2013) A posteriori L∞(L2)-error bounds in finite element approximation of the wave equation. IMA Journal of Numerical Analysis 33(4) pp. 1245-1264
- Lubich, C. and Makridakis, C., (2013). Interior a posteriori error estimates for time discrete approximations of parabolic problems, Numer. Math. 124, no. 3, 541-557.
- Makridakis, C. and Süli, E., (2013). Finite element analysis of Cauchy-Born approximations to atomistic models. Archive for Rational Mechanics and Analysis, 207 (3). pp. 813-843. ISSN 0003-9527
- Vairaktaris, E. and Makridakis, C., (2013). Control estimates and well-posedness of an inverse subsidence problem in geomechanics. Inverse Problems in Science and Engineering, 21 (5). pp. 823-839. ISSN 1741-5977.

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