42 citations · 118 across the 15 of their papers we have counts for
15 papers · 1 filter
A posteriori error analysis, Pod-Deim reduced order geometrically parametrized models and unfitted FEMs
Efthymios N. Karatzas
We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a param…
Boundary and distributed optimal control for a population dynamics PDE model with discontinuous in time Galerkin FEM schemes
EFthymios N. Karatzas
We consider fully discrete finite element approximations for a semilinear optimal control system of partial differential equations in two cases: for distributed and Robin boundary…
Reduced Basis, Embedded Methods and Parametrized Levelset Geometry
Efthymios N. Karatzas, Giovanni Stabile, Francesco Ballarin +1
In this chapter we examine reduced order techniques for geometrical parametrized heat exchange systems, Poisson, and flows based on Stokes, steady and unsteady incompressible Navie…
hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems
Efthymios N. Karatzas
In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on…
Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
Xianyi Zeng, Giovanni Stabile, Efthymios N. Karatzas +2
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background me…
Discrete Empirical Interpolation and unfitted mesh FEMs: application in PDE-constrained optimization
Georgios Katsouleas, Efthymios N. Karatzas, Fotios Travlopanos
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimizati…
A Reduced Order Cut Finite Element method for geometrically parameterized steady and unsteady Navier-Stokes problems
Efthymios N. Karatzas, Monica Nonino, Francesco Ballarin +1
This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition withi…
A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements
Efthymios N. Karatzas, Gianluigi Rozza
In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlin…
Equal higher order analysis of an unfitted discontinuous Galerkin method for Stokes flow systems
Aikaterini Aretaki, Efthymios N. Karatzas, Georgios Katsouleas
In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and…
Cut finite element error estimates for a class of nonlinear elliptic PDEs
Georgios Katsouleas, Efthymios N. Karatzas, Fotios Travlopanos
Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of intere…
Random geometries for optimal control PDE problems based on fictitious domain FEMS and cut elements
Aikaterini Aretaki, Efthymios N. Karatzas
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredien…
A Reduced-Order Shifted Boundary Method for Parametrized incompressible Navier-Stokes equations
Efthymios N. Karatzas, Giovanni Stabile, Leo Nouveau +2
We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded"…
Projection-based reduced order models for a cut finite element method in parametrized domains
Efthymios N. Karatzas, Francesco Ballarin, Gianluigi Rozza
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attracti…
A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to a Stokes Flow
Efthymios N. Karatzas, Giovanni Stabile, Leo Nouveau +2
We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to treat more complex parametrized dom…
A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries
E. N. Karatzas, G. Stabile, N. Atallah +2
A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat…