Research Activities :

Publications

• (E. N. Karatzas), “hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems”, submitted for publication, 2023, arXiv:2301.12577v1

• (E. N. Karatzas, G. Stabile, F. Ballarin, and G. Rozza), Book chapter In Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics: “Reduced Basis, Embedded Methods, and Parametrized Level-Set Geometry”, SIAM Computational Science and Engineering, 2022, doi:10.1137/1.9781611977257.ch13 ,

• (A. Aretaki, E. N. Karatzas), “Random geometries for optimal control PDE problems based on fictitious domain FEMS and cut elements”, Journal of Computational and Applied Mathematics, Vol. 412, 114-286, 2022, doi:10.1016/j.cam.2022.114286

• (X. Zeng, G. Stabile, E. N. Karatzas, G. Scovazzi, and G. Rozza), “Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method”, Computer Methods in Applied Mechanics and Engineering, 2022, doi:2022.115143

• (A. Aretaki, E. N. Karatzas, G. Katsouleas), “Equal higher order analysis on an unfitted dG method for Stokes flow systems”, Journal of Scientific Computing, 91, 48, 2022, doi:2006.00435

• (G. Katsouleas, E. N. Karatzas, F. Travlopanos), “Discrete Empirical Interpolation and unfitted mesh FEMs: application in PDE–constrained optimization”, Optimization Journal, 2022, doi:10.1080/02331934.2022.2032697

• (E. N. Karatzas and G. Rozza), “A Reduced Order Model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements”, Journal of Scientific Computing, 89, 9, 2021, DOI: 10.1007/s10915-021-01623-8

• (E. N. Karatzas, M. Nonino, F. Ballarin and G. Rozza), “A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems”, Computers & Mathematics with Applications, 2021, doi:10.1016/j.camwa.2021.07.016

• (E. N. Karatzas, G. Stabile, L. Nouveau, G. Scovazzi, and G. Rozza), “A Reduced Order Model for embedded domain computations Based on Shifted Boundary Method: Parametrized incompressible Navier-Stokes equations”, Computer Methods in Applied Mechanics and Engineering, 2020, doi:10.1016/j.cma.2020.113273

• (E. N. Karatzas, F. Ballarin, and G. Rozza), “Projection-based reduced order models for a cut finite element method in parametrized domains”, Computers & Mathematics with Applications, 2020, doi:10.1016/j.camwa.2019.08.003

• (E. N. Karatzas, G. Stabile, N. Atallah, G. Scovazzi, and G. Rozza), “A reduced order approach for the embedded shifted boundary FEM and a heat exchange system on parametrized geometries”, International Union of Theoretical and Applied Mechanics, Symposium on International Union of Theoretical and Applied Mechanics, Symposium on Model order reduction of coupled systems, 2020, arXiv:1807.07753 or doi:10.1007/978-3-030-21013-7_8

• (K. Chrysafinos, E. N. Karatzas and D. Kostas), “Stability and Error Estimates of Fully Discrete Schemes for the Brusselator System”, SIAM Journal on Numerical Analysis, 57:2, 828-853, 2019, doi:10.1137/18M1185594

• (E. N. Karatzas, G. Stabile, L. Nouveau, G. Scovazzi, and G. Rozza), “A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow”, Computer Methods in Applied Mechanics and Engineering 347, 568–587, 2019, doi:10.1016/j.cma.2018.12.040

• (G. Katsouleas, E. N. Karatzas, F. Travlopanos), “Cut finite element error estimates for a class of nonlinear elliptic PDEs”, Loughborough University, 2020, doi:10.17028/rd.lboro.12154854.v1 , extended arXiv arXiv:2003.06489

• (K. Chrysafinos, E. N. Karatzas) "Symmetric error estimates for discontinuous Galerkin time-stepping schemes for optimal control problems constrained to evolutionary Stokes equations" (pdf). Computational Optimization and Applications, Volume 60, Issue 3, pp 719-751, 2015, doi:10.1007/s10589-014-9695-3

• (K. Chrysafinos, E. N. Karatzas) "Error Estimates for Discontinuous Galerkin Time-Stepping Schemes for Robin Boundary Control Problems Constrained to Parabolic PDEs" (pdf). SIAM J. Numer. Anal., 52(6), 2837–2862, 2014, doi:10.1137/130943108

• (K. Chrysafinos, E. N. Karatzas) "Discontinuous Galerkin time-stepping schemes for Robin boundary control problems constrained to parabolic PDEs", IFAC Workshop on Control of Systems Governed by PDEs, 2013.

• (K. Chrysafinos, E. N. Karatzas) "Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic pdes" (pdf). Discr. Cont. Dynam. Syst., Ser. B, Vol 17 (5), 2012, pp 1473-1506, doi:10.3934/dcdsb.2012.17.1473Β 

Phd Thesis

• Optimal Control and Parabolic Problems, Numerical Analysis and Applications, http://dx.doi.org/10.26240/heal.ntua.1496 , (also here in Greek and English in one file), 2015.

Master Thesis

• Analysis and approximations of optimal control problems for evolutionary equations: basic concepts, some basic results, 2009 (pdf).
• Aeroacoustic research in the automotive industry - the antenna model - hyperbolic pdes, 2001 (pdf).

BSc Thesis

• Optimization and linear programming, 1999.

Research

• Projects (link)