Journal Papers
(Numerical Analysis for the numerical solution of PDEs and of Stochastic PDEs)
D.C. Antonopoulou, G. Karali, D. Li, Optimal error estimates of energy-stable Runge-Kutta methods for the ε-dependent Cahn-Hilliard/Allen-Cahn equation, accepted, Journal of Scientific Computing, 2025.
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, 44(3), pp. 1862--1902 , 2024. (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, G. Dewhirst, G. Karali, K. Tzirakis, Local existence of the outer parabolic Stochastic Stefan problem on the sphere, Journal of Differential Equations, 423, pp. 439--475, 2025. (pdf)
D.C. Antonopoulou, D. Farazakis, G. Karali, Existence of maximal solutions for the financial stochastic Stefan problem of a volatile asset with spread, Stochastic Processes and their Applications, 179, 2025. (pdf)
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)