Irene Sykopetritou

Ph.D Candidate - Teaching Assistant

Department of Mathematics and Statistics

University of Cyprus

Home: Welcome

195255591_158637556242223_1917811417273382037_n%20(2)_edited.jpg

CV

Irene Sykopetritou

Education and Studies

September 2018 - today

Doctoral studies in Applied Mathematics, Department of Mathematics and Statistics, University of Cyprus
(Thesis Advisor: Dr. Christos Xenophontos)

September 2016 - June 2018

M.Sc. in Applied Mathematics, Department of Mathematics and Statistics, University of Cyprus
(Thesis Advisor: Dr. Christos Xenophontos)

September 2012 - June 2016

B.Sc. in Mathematics (Applied Mathematics), Department of Mathematics and Statistics, University of Cyprus

Research Interests

Numerical Analysis, Finite Element Methods

Publications

Journal Articles

C. Xenophontos, S. Franz and I. Sykopetritou, Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters, Numerical Methods PDEs, Vol. 38, Num. 5, pp. 1543 - 1555 (2022).
I. Sykopetritou and C. Xenophontos, An hp finite element method for a singularly perturbed reaction-convection-diffusion boundary value problem with two small parameters, International Journal of Numerical Analysis and Modeling, Vol. 18, Num. 4, pp. 481 - 499 (2021).
C. Xenophontos and I. Sykopetritou, Isogeometric Analysis for singularly perturbed problems in 1-D: error estimates, Electronic Transactions on Numerical Analysis, Vol. 52, pp. 1 - 25 (2020).

Conferences' Participations

15th Annual Workshop on Numerical Methods for Problems with Layer Phenomena (Larnaca, 24-25 May 2018)
Contemporary Aspects of Analysis II (Protaras, 6-10 May 2019)
18th Annual Workshop on Numerical Methods for Problems with Layer Phenomena (Hagen, 24-26 March 2022)
European Finite Element Fair 2023 (Enschede, The Netherlands, 12-13 May 2023)
19th Annual Workshop on Numerical Methods for Problems with Layer Phenomena (Prague, 25-27 May 2023)

Advanced Courses

Advanced ECCOMAS Course Mathematical Theory of Finite Elements (Warsaw, 24-28 June 2019)

Home: CV

Published Work

Journal Articles

Isogeometric Analysis for singularly perturbed problems in 1-D : error estimates

ETNA, 2020

Christos Xenophontos and Irene Sykopetritou

Abstract. We consider one-dimensional singularly perturbed boundary value problems of reaction-convection-diffusion type, and the approximation of their solution using isogeometric analysis. In particular, we use a Galerkin formulation with B-splines as basis functions, defined on appropriately chosen knot vectors. We prove robust exponential convergence in the energy norm, independently of the singular perturbation parameters, and illustrate our findings through a numerical example.

An hp finite element method for a singularly perturbed reaction-convection-diffusion boundary value problem with two small parameters

IJNAM, 2021

Irene Sykopetritou and Christos Xenophontos

Abstract. We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the hp version of the Finite Element Method on the so-called Spectral Boundary Layer mesh. We show that the method converges uniformly, with respect to both singular perturbation parameters, at an exponential rate when the error is measured in the energy norm. Numerical examples are also presented, which illustrate our theoretical findings as well as compare the proposed method with others found in the literature.

Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters

NMPDE, 2022

Christos Xenophontos, Sebastian Franz and Irene Sykopetritou

Abstract. We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the hp version of the Finite Element Method on the Spectral Boundary Layer mesh. We use a mixed formulation requiring only C^0 basis functions in two-dimensional smooth domains. Under the assumption of analytic data, we show that the method converges uniformly, with respect to both singular perturbation parameters, at an exponential rate when the error is measured in the energy norm. Our theoretical findings are illustrated through numerical examples, including results using a stronger (balanced) norm.