# Dr Dimitra Antonopoulou

Dimitra graduated from the Department of Mathematics of University of Athens with a BSc degree in Mathematics in 1994. She received her MSc in Applied Mathematics - Numerical Analysis from the Department of Mathematics of University of Athens in 1999, and her PhD in Numerical Analysis from the Department of Mathematics of University of Athens in 2006. She joined the Department of Mathematics of University of Chester as a Senior Lecturer in December 2014.

## Qualifications

BSc, MSc, PhD, FHEA

## Overview

Before joining the University of Chester Dimitra held the following positions:

- 2012-2014: Research Fellow, Department of Mathematics and Applied Mathematics of University of Crete and IACM-FORTH, Heraklion, Greece.
- 2006-2012: Visiting Assistant Professor, Department of Applied Mathematics, University of Crete, Heraklion, Greece.
- 1996-2006: Assistant in laboratories and exercises of Numerical Analysis, Fortran, Matlab, Computational Mathematics, Calculus, Department of Mathematics, University of Athens, Greece.

Furthermore, Dimitra has held the following scholarships:

- National Scholarship for Postdoctoral Research, (2007--2008).
- Ph.D Scholarship (Marie Curie Fellowship), Department of Mathematics, University Paris-Sud, Orsay, France (1/2/2004 - 30/6/2004).
- National Scholarship (IKY) in Pure Mathematics-Analysis, Department of Mathematics, University of Athens, Greece, (1996 - 2000).
- Postgraduate Scholarship (Program ERASMUS), Department of Applied Mathematics, University of Versailles, France (1/6/1998 - 31/8/1998).

Dimitra is an AMS reviewer.

You can read more about Dimitra on her personal website, which may be found here.

- Shortcuts
- Teaching
- Research
- Published Work

## Teaching

Dimitra, was a Visiting Assistant Professor at the Department of Applied Mathematics, of University of Crete, in Heraklion, Greece for the period 2006-2012, where she was the responsible professor for Functional Analysis, Linear and Non-Linear Programming, Calculus, Numerical Solution of ODE, and Probability.

- Functional Analysis: Fall 2006, Fall 2007.
- Linear and Non-Linear Programming: Spring 2007, Spring 2008, Spring 2009, Spring 2010, Fall 2011.
- Calculus: Fall 2008, Fall 2009, Fall 2010.
- Numerical Solution of ODE: Spring 2011.
- Probability: Spring 2012.

During the period 1996-2006, Dimitra was Assistant at the Department of Mathematics of University of Athens, Greece, in laboratories and exercises of Numerical Analysis, Fortran, Matlab, Computational Mathematics, and Calculus.

## Research

Dimitra's research spans Analysis and Numerical Analysis of PDEs and Stochastic PDEs:

Finite Element Methods, Finite Difference Schemes, Discontinuous Galerkin Methods, Deterministic and Stochastic Non-linear Partial Differential Equations, Applied Functional Analysis, Multi-Phase Materials, Underwater Acoustics, Aeroacoustics.

Numerical Analysis of PDEs-SPDEs: Dimitra examines existence and uniqueness of numerical solutions, and a priori, a posteriori error estimates for initial and boundary value problems for evolutionary PDEs such as Heat, and Schroedinger equations (underwater acoustics and aeroacoustics). The numerical solution of the approximating schemes is implemented by Fortran codes. Furthermore, Dimitra analyzes continuous and DG finite element methods for non-linear Stochastic PDEs stemming from phase separation (multi-phase materials).

Analysis of PDEs-SPDEs: Dimitra also works on the asymptotic analysis and dynamics of stochastic and deterministic problems in phase transitions such as the stochastic and deterministic Cahn-Hilliard and Allen-Cahn equations, the free boundary Stefan problem of Ostwald ripening, the volume preserving mean curvature flow and the stochastic motion under mean curvature flow. In addition, Dimitra considers certain Riemann-Hilbert problems arising from non-linear PDEs such as the NLS equation and studies rigorously the long time asymptotics of solutions.

## Published work

**Journal papers**

- (with S. Kamvissis) Addendum to the article: On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line, Nonlinearity, 29(10), pp. 3206--3214, 2016.
- (with P.W. Bates, D. Blömker, G.D. Karali) Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation, SIAM J. Math. Anal., 48-1, pp. 670--708, 2016.
- (with G.D. Karali, A. Millet) Existence and regularity of solution for a stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion, J. Differential Equations 260 (2016) 2383–2417.
- (with S. Kamvissis) On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line, Nonlinearity, 28, pp. 3073--3099, 2015
- Galerkin methods for a Schrödinger-type equation with a dynamical boundary condition in two dimensions, ESAIM: M2AN, 49(4), pp. 1127--1156, 2015
- (with G.D. Karali, M. Plexousakis, G.E. Zouraris) Crank-Nicolson Finite Element Discretizations for a 2D Linear Schrödinger-Type Equation Posed in a Noncylindrical Domain, Mathematics of Computation, 84(294), pp. 1571--1598, 2015
- (with G.D. Karali, E. Orlandi) A Hilbert expansions method for the rigorous sharp interface limit of the generalized Cahn-Hilliard Equation, Interfaces and Free Boundaries, 16(1), pp. 65--104, 2014.
- (with G.D. Karali) A nonlinear partial differential equation for the volume preserving mean curvature flow, Networks and Heterogeneous Media, 8(1), pp. 9--22, 2013.
- (with V.A. Dougalis, G.E. Zouraris) A Finite Difference method for the Wide-Angle `Parabolic' equation in a waveguide with downsloping bottom, Numer. Meth. PDEs, 29, pp. 1416--1440, 2013.
- (with D. Bloemker, G.D. Karali) Front motion in the one-dimensional stochastic Cahn-Hilliard equation, SIAM J. Math. Anal., 44-5, pp. 3242—3280, 2012.
- (with G.D. Karali, A.N.K. Yip) On the parabolic Stefan problem for Ostwald ripening with kinetic undercooling and inhomogeneous driving force, J. Differential Eq., 252, pp. 4679--4718, 2012.
- (with N.A. Kampanis, A.I. Delis, G. Kozyrakis) A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates, published on line in Appl. Numer. Math., 2011 (doi:10.1016/j.apnum.2011.05.005).
- Galerkin methods for the `Parabolic Equation' Dirichlet problem in a variable 2-D and 3-D topography, published on line in Appl. Numer. Math., 2011 (doi:10.1016/j.apnum.2011.04.002).
- (with G.D. Karali, G.T. Kossioris) Asymptotics for a generalized Cahn-Hilliard equation with forcing terms, Discrete Contin. Dyn. Syst. A, 30(4), pp. 1037--1054, 2011.
- (with G.D. Karali) Existence of solution for a generalized Stochastic Cahn-Hilliard Equation on convex domains, Discrete Contin. Dyn. Syst. B, 16(1), pp. 31--55, 2011.
- (with G.D. Karali, I.M. Sigal) Stability of spheres under volume-preserving mean curvature flow, Dynamics of PDE, 7(4), pp. 327--344, 2010.
- (with M. Plexousakis) Discontinuous Galerkin Methods for the Linear Schroedinger Equation in non-cylindrical domains, Numer. Math., 115(4), pp. 585--608, 2010.
- (with V.A. Dougalis, G.E. Zouraris) Galerkin methods for Parabolic and Schroedinger Equations with dynamical boundary conditions and applications to underwater acoustics, SIAM J. Numer. Anal., 47(4), pp. 2752--2781, 2009.

**Conference Papers and Other**

- (with V.A. Dougalis, F. Sturm, G.E. Zouraris) Conservative initial-boundary problems for the Wide-Angle PE in waveguides with variable bottoms, Proceedings Acoustics'08 Paris, J. Acoust. Soc. Am., 123 (2008), pp. 3598.
- (with V.A. Dougalis, G.E. Zouraris) A finite element method for the PE in a variable, rigid bottom environment, via a model reformulation, Proceedings, ICTCA07, IACM-FORTH, 2007.
- (with V.A. Dougalis, G.E. Zouraris) Finite element discretization of the PE in domains with a variable, rigid bottom, Proceedings, ELINA 2006, IACM-FORTH.
- (with V.A. Dougalis) A Discontinuous Galerkin Method for the Linear Schroedinger Equation in a variable domain, Proceedings, 36me Congr. National d'Analyse Num. Obernai (Bas-Rhin, Alsace), 2004.
- (with V.A. Dougalis) Finite Element Discretization of the "Parabolic" Equation in an underwater variable bottom environment, Advances in Scattering and Biomedical Engineering, World Scientific, New Jersey, eds. D. Fotiadis and C. Massalas, pp. 173--182, 2004.
- (with A. Antonopoulos) Pedal hyper-surfaces and DOP factors in GPS, Survey Review, 38(296), pp. 138--145, 2005.
- (with A. Antonopoulos) Remarks on the stability of satellite motion, Artificial satellites, Journal of Planetary Geodesy, 37(3), pp. 97--108, 2002.

Downloadable copies of many of Dimitra's publications can be found on her personal website here.