Charalambos Makridakis
Director of the Institute of Applied and Computational Mathematics
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Professor Makridakis holds the post of Professor of Numerical Analysis at the University of Crete and of Professor of Mathematics at the University of Sussex (on leave). He was founding member of the Department of Applied Mathematics and of the Archimedes Center for Modelling, Analysis and Computation in Crete. He had active role in leading European network grants related to Nonlinear Partial Differential Equations and their Applications funded by the European Commission. He received his PhD from the University of Crete in 1990; subsequently he was a post-doc at the University of Maryland, College Park and at the University of Tennessee. He held short term visiting posts at several universities and centres, including, Institute for Pure and Applied Mathematics at UCLA, University of Oxford, École Normale Superieure-Paris, CIRM-France, Institut Mittag-Leffler-Sweden and University of Rennes. Professor Makridakis is member of the Editorial Board of IMA Journal of Numerical Analysis and coordinator of the International Network 'Modelling and Computations for Shocks and Interfaces’.
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CURRENT RESEARCH INTERESTS• Multiscale Adaptive Modeling and Algorithms– Static atomistic/continuum coupling– Dynamic atomistic/continuum coupling– Kinetic/continuum coupling– Coarse grained time integrators– Multiscale methods for the Helmholtz equation• Adaptive Methods for Evolutionary Problems– Error control driven algorithms, a posteriori estimates– Geometric/Anisotropic adaptivity– Convergence of adaptive algorithms– Space-time adaptivity• Wave Propagation Problems– Shock-wave propagation problems– DG methods for linear transport– Error control for wave equations– Computational methods for dispersive wave equations– Computational methods for high frequency wave propagation problems• Problems in Fluid Mechanics.– Error control for Navier-Stokes– Efficient solvers for Navier-Stokes: non-standard time discretizations (fractional step, projection methods)– Adaptive methods for turbulent models– Isothermal Navier-Stokes Korteweg system • Material Defects – Computational methods for material defects for static problems– Computational methods for dynamic crack growth and dislocation motion
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Selected Articles
Makridakis, Charalambos G (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
Georgoulis, Emmanuil H, Hall, Edward and Makridakis, Charalambos (2017) An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems. IMA Journal of Numerical Analysis. ISSN 0272-4979
Georgoulis, Emmanuil H, Lakkis, Omar, Makridakis, Charalambos G and Virtanen, Juha M (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
Lakkis, Omar, Makridakis, Charalambos and Pryer, Tristan (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
Giesselmann, Jan, Makridakis, Charalambos and Pryer, Tristan (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, Ohannes and Makridakis, Charalambos (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
Giesselmann, Jan, Makridakis, Charalambos and Pryer, Tristan (2014) Energy consistent DG methods for the Navier-Stokes-Korteweg system. Mathematics of Computation, 83 (289). pp. 2071-2099. ISSN 0025-5718
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
Makridakis, Charalambos and Süli, Endre (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
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
Kyza, Irene and Makridakis, Charalambos (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
Akrivis, George, Makridakis, Charalambos and Nochetto, Ricardo 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