Implicit-explicit multistep finite element methods for nonlinear parabolic problems. - Georgios Akrivis; Michel Crouzeix; Charalambos G. Makridakis (Math. Comput., 1998)

A space-time finite element method for the nonlinear Schröinger equation: the discontinuous Galerkin method. - Ohannes A. Karakashian; Charalambos G. Makridakis (Math. Comput., 1998)

Implicit-explicit multistep methods for quasilinear parabolic equations. - Georgios Akrivis; Michel Crouzeix; Charalambos G. Makridakis (Numerische Mathematik, 1999)

Finite volume schemes for Hamilton-Jacobi equations. - Georgios Kossioris; Charalambos G. Makridakis; Panagiotis E. Souganidis (Numerische Mathematik, 1999)

Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws. - Laurent Gosse; Charalambos G. Makridakis (SIAM J. Numer. Anal., 2000)

Finite volume relaxation schemes for multidimensional conservation laws. - Theodoros Katsaounis; Charalambos G. Makridakis (Math. Comput., 2001)

Optimal Rate of Convergence for Anisotropic Vanishing Viscosity Limit of a Scalar Balance Law. - Charalambos G. Makridakis; Benoît Perthame (SIAM J. Math. Anal., 2003)

Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems. - Charalambos G. Makridakis; Ricardo H. Nochetto (SIAM J. Numer. Anal., 2003)

Sharp CFL, Discrete Kinetic Formulation, and Entropic Schemes for Scalar Conservation Laws. - Charalambos G. Makridakis; Benoit Perthame (SIAM J. Numer. Anal., 2003)

Stability and Convergence of a Class of Finite Element Schemes for Hyperbolic Systems of Conservation Laws. - Christos Arvanitis; Charalambos G. Makridakis; Athanasios E. Tzavaras (SIAM J. Numer. Anal., 2004)

Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations. - Ohannes A. Karakashian; Charalambos G. Makridakis (Math. Comput., 2005)

A posteriori error estimates for the Crank-Nicolson method for parabolic equations. - Georgios Akrivis; Charalambos G. Makridakis; Ricardo H. Nochetto (Math. Comput., 2006)

Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems. - Omar Lakkis; Charalambos G. Makridakis (Math. Comput., 2006)

A posteriori error analysis for higher order dissipative methods for evolution problems. - Charalambos G. Makridakis; Ricardo H. Nochetto (Numerische Mathematik, 2006)

Error Control for a Class of Runge-Kutta Discontinuous Galerkin Methods for Nonlinear Conservation Laws. - Andreas Dedner; Charalambos G. Makridakis; Mario Ohlberger (SIAM J. Numer. Anal., 2007)

A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces. - Eduardo Cuesta; Charalambos G. Makridakis (Numerische Mathematik, 2008)

Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods. - Georgios Akrivis; Charalambos G. Makridakis; Ricardo H. Nochetto (Numerische Mathematik, 2009)

A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems. - Alan Demlow; Omar Lakkis; Charalambos G. Makridakis (SIAM J. Numer. Anal., 2009)

Sharply local pointwise a posteriori error estimates for parabolic problems. - Alan Demlow; Charalambos G. Makridakis (Math. Comput., 2010)

Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence. - Georgios Akrivis; Charalambos G. Makridakis; Ricardo H. Nochetto (Numerische Mathematik, 2011)

A priori error analysis of two force-based atomistic/continuum models of a periodic chain. - Charalambos G. Makridakis; Christoph Ortner; Endre Süli (Numerische Mathematik, 2011)

Analysis for Time Discrete Approximations of Blow-up Solutions of Semilinear Parabolic Equations. - Irene Kyza; Charalambos G. Makridakis (SIAM J. Numer. Anal., 2011)

Helmholtz Equation with Artificial Boundary Conditions in a Two-Dimensional Waveguide. - D. A. Mitsoudis; Charalambos G. Makridakis; Michael Plexousakis (SIAM J. Math. Anal., 2012)

A Posteriori Error Control for Fully Discrete Crank-Nicolson Schemes. - Eberhard Bänsch; Fotini Karakatsani; Charalambos G. Makridakis (SIAM J. Numer. Anal., 2012)

Interior a posteriori error estimates for time discrete approximations of parabolic problems. - Christian Lubich; Charalambos G. Makridakis (Numerische Mathematik, 2013)

Energy consistent discontinuous Galerkin methods for the Navier-Stokes-Korteweg system. - Jan Giesselmann; Charalambos G. Makridakis; Tristan Pryer (Math. Comput., 2014)

A posteriori error estimates for discontinuous Galerkin methods for the generalized Korteweg-de Vries equation. - Ohannes A. Karakashian; Charalambos G. Makridakis (Math. Comput., 2015)

A comparison of duality and energy a posteriori estimates for L∞(0, T;L2(Ω)) in parabolic problems. - Omar Lakkis; Charalambos G. Makridakis; Tristan Pryer (Math. Comput., 2015)

A Posteriori Analysis of Discontinuous Galerkin Schemes for Systems of Hyperbolic Conservation Laws. - Jan Giesselmann; Charalambos G. Makridakis; Tristan Pryer (SIAM J. Numer. Anal., 2015)

A Posteriori Error Estimates for Leap-Frog and Cosine Methods for Second Order Evolution Problems. - Emmanuil H. Georgoulis; Omar Lakkis; Charalambos G. Makridakis; Juha M. Virtanen (SIAM J. Numer. Anal., 2016)

On the Babuška-Osborn approach to finite element analysis: (L^2 ) estimates for unstructured meshes. - Charalambos G. Makridakis (Numerische Mathematik, 2018)

Approximations of cell-induced phase transitions in fibrous biomaterials: Γ-convergence analysis. - Georgios Grekas; Konstantinos Koumatos; Charalambos G. Makridakis; Phoebus Rosakis (CoRR, 2019)

A new class of entropy stable schemes for hyperbolic systems: Finite element methods. - Ioannis Gkanis; Charalambos G. Makridakis (Math. Comput., 2021)

A posteriori error analysis for approximations of time-fractional subdiffusion problems. - Lehel Banjai; Charalambos G. Makridakis (Math. Comput., 2022)

A posteriori error estimates for Radau IIA methods via maximal parabolic regularity. - Georgios Akrivis; Charalambos G. Makridakis (Numerische Mathematik, 2022)

On Maximal Regularity Estimates for Discontinuous Galerkin Time-Discrete Methods. - Georgios Akrivis; Charalambos G. Makridakis (SIAM J. Numer. Anal., 2022)

Approximations of Energy Minimization in Cell-Induced Phase Transitions of Fibrous Biomaterials: $ Gamma$-Convergence Analysis. - Georgios Grekas; Konstantinos Koumatos; Charalambos G. Makridakis; Phoebus Rosakis (SIAM J. Numer. Anal., 2022)

A new approach to generalisation error of machine learning algorithms: Estimates and convergence. - Michail Loulakis; Charalambos G. Makridakis (CoRR, 2023)

On the Stability and Convergence of Physics Informed Neural Networks. - Dimitrios Gazoulis; Ioannis Gkanis; Charalambos G. Makridakis (CoRR, 2023)

Deep Ritz - Finite Element methods: Neural Network Methods trained with Finite Elements. - Georgios Grekas; Charalambos G. Makridakis (CoRR, 2024)

Deep Uzawa for PDE constrained optimisation. - Charalambos G. Makridakis; Aaron Pim; Tristan Pryer (CoRR, 2024)

A Deep Uzawa-Lagrange Multiplier Approach for Boundary Conditions in PINNs and Deep Ritz Methods. - Charalambos G. Makridakis; Aaron Pim; Tristan Pryer (CoRR, 2024)

Runge-Kutta Physics Informed Neural Networks: Formulation and Analysis. - Georgios Akrivis; Charalambos G. Makridakis; Costas Smaragdakis (CoRR, 2024)

Compressive instabilities enable cell-induced extreme densification patterns in the fibrous extracellular matrix: Discrete model predictions. - Chrysovalantou Kalaitzidou; Georgios Grekas; Andreas Zilian; Charalambos G. Makridakis; Phoebus Rosakis (PLoS Comput. Biol., 2024)

A class of discontinuous Galerkin methods for nonlinear variational problems. - Georgios Grekas; Konstantinos Koumatos; Charalambos G. Makridakis; Andreas Vikelis (Math. Comput., 2025)

Convergence of Discontinuous Galerkin Methods for Quasiconvex and Relaxed Variational Problems. - Georgios Grekas; Konstantinos Koumatos; Charalambos G. Makridakis; Andreas P. Vikelis (CoRR, 2025)

A generative modeling / Physics-Informed Neural Network approach to random differential equations. - Georgios Arampatzis; Stylianos Katsarakis; Charalambos G. Makridakis (CoRR, 2025)

PINN-DG: Residual neural network methods trained with Finite Elements. - Georgios Grekas; Charalambos G. Makridakis; Tristan Pryer (CoRR, 2025)

Deep Uzawa for Kinetic Transport with Lagrange-Enforced Boundaries. - Charalambos G. Makridakis; Aaron Pim; Tristan Pryer; Nikolaos Rekatsinas (CoRR, 2025)