Research Interests

• finite element methods for SPDEs
• adaptive methods for SDEs
• numerical methods for nonlinear pdes
• numerical methods for mean field problems

Journal Publications

• Implicit-Explicit Finite Difference Approximations of a Semilinear Heat Equation with Logarithmic Nonlinearity
  (with P. Paraschis), Computational Methods in Applied Mathematics (accepted on February 14, 2023).
  
• Error Estimation of the Relaxation Finite Difference Scheme for the Nonlinear Schrödinger Equation.
  SIAM Journal on Numerical Analysis 61 (2023), no. 1, 365-397.
  
• On the convergence of the Crank-Nicolson method for the logarithmic Schrödinger equation
  (with P. Paraschis), Discrete and Continuous Dynamical Systems-Series B 28 (2023), no. 1, 245-261.
  
• Error Estimation of the Besse Relaxation Scheme for a Semilinear Heat Equation.
  Mathematical Modelling and Numerical Analysis 55 (2021), no. 1, 301-328.
  
• An IMEX finite element method for a linearized Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise.
  Computational and Applied Mathematics 37 (2018), no. 5, 5555-5575.
  
• A linear implicit finite difference discretization of the Schrödinger-Hirota equation.
  Journal of Scientific Computing 77 (2018), no. 1, 634-656.
  
• Crank-Nicolson finite element approximations for a linear stochastic fourth order equation with additive space-time white noise.
  SIAM Journal on Numerical Analysis 56 (2018), no. 2, 838-858.
  
• Crank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain,
  (with D. Antonopoulou, G. Karali and M. Plexousakis), Mathematics of Computations 84 (2015), no. 294, 1571-1598.
  
• Finite Element Approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise,
  (with G. Kossioris) Discrete and Continuous Dynamical Systems-Series B 18 (2013), no. 7, 1845-1872.
  
• Monte Carlo Euler approximations of HJM term structure financial models,
  (with T. Björk, A. Szepessy and R. Tempone), BIT Numerical Mathematics 53 (2013), no. 2, 341-383.
  
• A finite difference method for the wide-angle `parabolic' equation in a waveguide with downsloping bottom,
  (with D. Antonopoulou and V. Dougalis), Numerical Methods for Partial Differential Equations 29 (2013), no. 4, 1416-1440.
  
• Finite element approximations for a linear fourth-order parabolic SPDE in two and three space dimensions with additive space-time white noise,
  (with G. Kossioris), Applied Numerical Mathematics 67 (2013), Special Issue: NUMAN 2010, 243-261.
  
• Theory and numerical approximations for a nonlinear 1+1 Dirac system,
  (with N. Bournaveas), Mathematical Modelling and Numerical Analysis 46 (2012), no. 4, 841-874.
  
• Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise,
  (with G. Kossioris), Mathematical Modelling and Numerical Analysis 44 (2010), no. 2, 289-322.
  
• Galerkin methods for parabolic and Schrödinger equations with dynamical boundary conditions and applications to underwater acoustics,
  (with D. Antonopoulou and V. Dougalis), SIAM Journal on Numerical Analysis 47 (2009), no. 4, 2752-2781.
  
• On an initial-boundary value problem for a wide-angle parabolic equation in a waveguide with a variable bottom,
  (with V. Dougalis and F. Sturm), Mathematical Methods in the Applied Sciences 32 (2009), no. 12, 1519-1540.
  
• A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves,
  (with P. Xanthopoulos), Discrete and Continuous Dynamical Systems-Series B 10 (2008), no. 1, 239-263.
  
• Adaptive weak approximation of diffusions with jumps,
  (with E. Mordecki, A. Szepessy and R. Tempone), SIAM Journal on Numerical Analysis 46 (2008), no. 4, 1732-1768.
  
• Numerical solution of a non-local elliptic problem modeling a thermistor with a finite element and a finite volume method,
  (with C. Nikolopoulos), Discrete and Continuous Dynamical Systems-Supplements (2007), vol. 2007, Special Issue, 768-778.
  
• Convergence rates for adaptive weak approximation of stochastic differential equations,
  (with K.-S. Moon, A. Szepessy and R. Tempone), Stochastic Analysis and Applications 23 (2005), no. 3, 511-558.
  
• Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation,
  (with I. Babuska and R. Tempone), Computer Methods in Applied Mechanics and Engineering 194 (2005), no. 12-16 ,1251-1294.
  
• On the construction and analysis of high order locally conservative finite volume-type methods for one-dimensional elliptic problems,
  (with M. Plexousakis), SIAM Journal on Numerical Analysis 42 (2004), no. 3, 1226-1260.
  
• Galerkin finite element approximations of stochastic elliptic partial differential equations,
  (with I. Babuska and R. Tempone), SIAM Journal on Numerical Analysis 42 (2004), no.2, 800-825.
  
• A variational principle for adaptive approximations of ordinary differential equations,
  (with K.-S. Moon, A. Szepessy and R. Tempone), Numerische Mathematik 96 (2003), no. 1, 131-152.
  
• Convergence rates for adaptive approximation of ordinary differential equations,
  (with K.-S. Moon, A. Szepessy and R. Tempone), Numerische Mathematik 96 (2003), no.1, 99-129.
  
• Adaptive weak approximation of stochastic differential equations,
  (with A. Szepessy and R. Tempone), Communications on Pure and Applied Mathematics 54 (2001), no. 10, 1169-1214.
  
• Finite difference schemes for the `parabolic' equation in a variable depth environment with a rigid bottom boundary condition,
  (with G. D. Akrivis and V. A. Dougalis), SIAM Journal on Numerical Analysis 39 (2001), no. 2, 539-565.
  
• On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation,
  Mathematical Modelling and Numerical Analysis 35 (2001), no. 3, 389-405.
  
• Convergence of Runge-Kutta approximations for parabolic problems with Neumann boundary conditions,
  Numerische Mathematik 77 (1997), no. 1, 123-142.
  
• Error estimates for finite difference methods for a wide-angle `parabolic' equation,
  (with G. D. Akrivis and V. A. Dougalis), SIAM Journal on Numerical Analysis 33 (1996), no. 6, 2488-2509.
  

Preprints

• Backward Euler finite difference approximations of a logarithmic heat equation over a 2D rectangular domain.
  hal-03220015 (May 6, 2021).
  
• Crank-Nicolson finite element approximations for a linear stochastic heat equation with additive space-time white noise.
  arXiv:1709.08496 (September 22, 2017)