Publications-Preprints

Journal Papers

(Numerical Analysis for the numerical solution of PDEs and of Stochastic PDEs)

D.C. Antonopoulou, B. Egwu, Y. Yan, A posteriori error analysis of space-time discontinuous Galerkin methods for the $\eps$-stochastic Allen-Cahn equation, IMA J. Num. Analysis, 2023, doi.org/10.1093/imanum/drad052. (pdf)
D.C. Antonopoulou, M. Bitsaki, G.D. Karali, The multi-dimensional Stochastic Stefan Financial Model for a portfolio of assets, Discrete Contin. Dyn. Syst. B, 4, pp. 1955--1987, 2022.(pdf)
D.C. Antonopoulou, L. Banas, R. Nurnberg, A. Prohl, Numerical approximation of the Stochastic Cahn-Hilliard equation near the sharp interface limit, Numer. Math., 147(3), pp. 505--551, 2021. (pdf),(pdf)
D.C. Antonopoulou, Space–time discontinuous Galerkin methods for the $\eps$-dependent stochastic Allen–Cahn equation with mild noise, IMA J. Num. Analysis, 40, pp. 2076--2105, 2020. (pdf)
D.C. Antonopoulou, M. Plexousakis, A posteriori analysis for space-time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain, ESAIM: M2AN, 53(2), pp. 523--549, 2019. (pdf)
D.C. Antonopoulou, Galerkin methods for a Schrödinger-type equation with a dynamical boundary condition in two dimensions, ESAIM: M2AN, 49(4), pp. 1127--1156, 2015.(pdf)
D.C. Antonopoulou, 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. (pdf)
D.C. Antonopoulou, 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. (pdf)
D.C. Antonopoulou, 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. (pdf)
N.A. Kampanis, A.I. Delis, D.C. Antonopoulou, G. Kozyrakis, A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates, Appl. Numer. Math., 67, pp. 152--166, 2013. (pdf)
D.C. Antonopoulou, Galerkin methods for the `Parabolic Equation' Dirichlet problem in a variable 2-D and 3-D topography, Appl. Numer. Math., 67, pp. 17--34, 2013. (pdf)
D.C. Antonopoulou, M. Plexousakis, Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains, Numer. Math., 115(4), pp. 585--608, 2010. (pdf)
D.C. Antonopoulou, V.A. Dougalis, G.E. Zouraris, Galerkin methods for Parabolic and Schrödinger Equations with dynamical boundary conditions and applications to underwater acoustics, SIAM J. Numer. Anal., 47(4), pp. 2752--2781, 2009. (pdf)

Journal Papers

(Analysis of PDEs and of Stochastic PDEs)

D.C. Antonopoulou, Higher moments for the Stochastic Cahn - Hilliard Equation with multiplicative Fourier noise, Nonlinearity, 36 , pp. 1053–-1081, 2023. (pdf)
D.C. Antonopoulou, G.D. Karali, K. Tzirakis, Layer Dynamics for the one dimensional $\eps$-dependent Cahn-Hilliard / Allen-Cahn Equation, Calculus of Variations and PDEs, 60(6), 207, 2021 (pdf)
D.C. Antonopoulou, D. Farazakis, G.D. Karali, Malliavin Calculus for the stochastic Cahn- Hilliard/Allen-Cahn equation with unbounded noise diffusion, Journal of Differential Equations, 265(7), pp. 3168--3211, 2018. (pdf)
D.C. Antonopoulou, D. Blömker, G.D. Karali, The sharp interface limit for the stochastic Cahn-Hilliard equation, Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 54(1), pp. 280--298, 2018. (pdf)
D.C. Antonopoulou, 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. (pdf) (pdf)
D.C. Antonopoulou, 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. (pdf)
D.C. Antonopoulou, 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, pp. 2383--2417, 2016. (pdf) (pdf)
D.C. Antonopoulou, 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. (pdf)
D.C. Antonopoulou, 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. (pdf)
D.C. Antonopoulou, D. Blömker, G.D. Karali, Front motion in the one-dimensional stochastic Cahn-Hilliard equation, SIAM J. Math. Anal., 44-5, pp. 3242--3280, 2012. (pdf)
D.C. Antonopoulou, G.D. Karali, A.N.K. Yip, On the parabolic Stefan problem for Ostwald ripening with kinetic undercooling and inhomogeneous driving force, Journal of Differential Equations, 252, pp. 4679--4718, 2012. (pdf)
D.C. Antonopoulou, 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. (pdf)
D.C. Antonopoulou, 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. (pdf)
D.C. Antonopoulou, G.D. Karali, I.M. Sigal, Stability of spheres under volume-preserving mean curvature flow, Dynamics of PDE, 7(4), pp. 327--344, 2010. (pdf)

Preprints

- 1. M. Alfaro, D.C. Antonopoulou, G.D. Karali, H. Matano, Generation of fine transition layers and their dynamics for the stochastic Allen-Cahn equation. (pdf)
  2. D.C. Antonopoulou, D. Farazakis, G. Karali, Existence of maximal solutions for the financial stochastic Stefan problem of a volatile asset with spread. (pdf)
  3. D.C. Antonopoulou, G. Karali, D. Li, Linearized Runge-Kutta methods for the $\eps$-dependent Cahn-Hilliard/Allen-Cahn equation.