Selected Articles
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)
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)
G Grekas, K Koumatos, C Makridakis, A Vikelis (2023) A class of Discontinuous Galerkin methods for nonlinear variational problems, arXiv preprint arXiv:2308.12891
D Gazoulis, I Gkanis, CG Makridakis (2023) On the Stability and Convergence of Physics Informed Neural Networks, arXiv preprint arXiv:2308.05423
M Loulakis, CG Makridakis (2023) A new approach to generalisation error of machine learning algorithms: Estimates and convergence, arXiv preprint arXiv:2306.13784
EH Georgoulis, CG Makridakis (2023) Lower bounds, elliptic reconstruction and a posteriori error control of parabolic problems, IMA Journal of Numerical Analysis, drac080 (html file)
C Kalaitzidou, G Grekas, A Zilian, C Makridakis, P Rosakis (2022) Compressive Instabilities Enable Cell-Induced Extreme Densification Patterns in the Fibrous Extracellular Matrix: Discrete Model Predictions, arXiv preprint arXiv:2212.01213
L Banjai, C Makridakis (2022) A posteriori error analysis for approximations of time-fractional subdiffusion problems, Mathematics of Computation 91 (336), 1711-1737 (pdf file)
L. Banjai, C Makridakis (2022) A posteriori error analysis for approximations of time-fractional subdiffusion problems, arXiv preprint arxiv.2203.00340
G Akrivis, CG Makridakis (2022) A posteriori error estimates for Radau IIA methods via maximal parabolic regularity, Numerische Mathematik 150 (3), 691-717 (html file)
G Akrivis, C Makridakis (2022) On maximal regularity estimates for discontinuous Galerkin time-discrete methods, SIAM Journal on Numerical Analysis 60 (1), 180-194 (html file)
G Grekas, K Koumatos, C Makridakis, P Rosakis (2022) Approximations of Energy Minimization in Cell-Induced Phase Transitions of Fibrous Biomaterials: Gamma-Convergence Analysis, SIAM Journal on Numerical Analysis 60 (2), 715-750 (pdf file)
I Gkanis, C Makridakis (2021) A new class of entropy stable schemes for hyperbolic systems: Finite element methods, Mathematics of Computation 90 (330), 1663-1699 (pdf file)
G Grekas, M Proestaki, P Rosakis, J Notbohm, C Makridakis, G Ravichandran (2021) Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix, Journal of the Royal Society Interface 18 (175), 20200823 (pdf file)
I Gkanis, G Grekas, E Karnessis, CG Makridakis (2020) Mathematics of computational modelling: some challenges of computing nonlinear phenomena, First Congress of Greek Mathematicians: Proceedings of the Congress held in Athens, Greece, June 25–30, 2018 (html file)
G Grekas, M Proestaki, P Rosakis, J Notbohm, C Makridakis, G Ravichandran (2019) Cells exploit a phase transition to establish interconnections in fibrous extracellular matrices, arXiv preprint arXiv:1905.11246
Grekas G, Koumatos K, Makridakis C, Rosakis P (2019) Approximations of energy minimization in cell-induced phase transitions of fibrous biomaterials: Gamma-convergence analysis, arXiv preprint arXiv:1907.01382
EH Georgoulis, E Hall, C Makridakis (2019) An a posteriori error bound for discontinuous Galerkin approximations of convection–diffusion problems, IMA Journal of Numerical Analysis 39 (1), 34-60 (html file) (pdf file)
E Baensch, F Karakatsani, CG Makridakis (2018) A posteriori error estimates for fully discrete schemes for the time dependent Stokes problem, Calcolo 55, 1-32 (html file)
Makridakis, CG (2018) On the Babuška-Osborn approach to finite element analysis: L2 estimates for unstructured meshes. Numerische Mathematik, 139 (4). pp. 831-844. ISSN 0029-599X (pdf file )
Georgoulis, EH, Hall, E and Makridakis, C (2017) An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems. IMA Journal of Numerical Analysis. ISSN 0272-4979 (pdf file)
Georgoulis, EH, Lakkis, O, Makridakis, CG and Virtanen, JM (2016) A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. SIAM Journal on Numerical Analysis (SINUM), 54 (1). pp. 120-136. ISSN 0036-1429 (pdf file)
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. Mathematics of Computation, 84 (294). pp. 1537-1569. ISSN 0025-5718 (pdf file)
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 (pdf file)
Karakashian, O and Makridakis, C (2014) A posteriori error estimates for discontinuous Galerkin Methods for the Generalised Korteweg-de Vries Equation. Mathematics of Computation, 84. pp. 1145-1167. ISSN 0025-5718 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
Bänsch, E, Karakatsani, F and Makridakis, C (2012) A posteriori error control for fully discrete Crank–Nicolson schemes. SIAM Journal on Numerical Analysis, 50 (6). pp. 2845-2872. ISSN 0036-1429 (pdf file)
Kyza, I and Makridakis, C (2011) Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations. SIAM Journal on Numerical Analysis, 49 (1). pp. 405-426. ISSN 0036-1429 (pdf file)
Akrivis, G, Makridakis, C and Nochetto, R H (2009) Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods. Numerische Mathematik, 114 (1). pp. 133-160. ISSN 0029-599X (pdf file)