106 citations · 162 across the 15 of their papers we have counts for
8 papers · 1 filter
Efficient numerical approximations for a non-conservative Nonlinear Schrodinger equation appearing in wind-forced ocean waves
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza
We consider a non-conservative nonlinear Schrodinger equation (NCNLS) with time-dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy…
Optimization Methods for One Dimensional Elastodynamics
Theodoros Katsaounis, Grigorios Kounadis, Ioanna Mousikou +1
We propose a new approach for solving systems of conservation laws that admit a variational formulation of the time-discretized form, and encompasses the p-system or the system of…
A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza +1
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrödinger-Poisson system. More specifically, we use the Cr…
A regularized shallow-water waves system with slip-wall boundary conditions in a basin: Theory and numerical analysis
Samer Israwi, Henrik Kalisch, Theodoros Katsaounis +1
The simulation of long, nonlinear dispersive waves in bounded domains usually requires the use of slip-wall boundary conditions. Boussinesq systems appearing in the literature are…
Boussinesq-Peregrine water wave models and their numerical approximation
Theodoros Katsaounis, Dimitrios Mitsotakis, George Sadaka
In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq syst…
On the reflection of solitons of the nonlinear Schrodinger equation
Theodoros Katsaounis, Dimitrios Mitsotakis
In this paper we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D nonlinear Schrodinger equation as the underlying m…
A posteriori error analysis for evolution nonlinear Schrödinger equations up to the critical exponent
Theodoros Katsaounis, Irene Kyza
We provide a posteriori error estimates in the norm for relaxation time discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger equations…
A posteriori error control & adaptivity for Crank-Nicolson finite element approximations for the linear Schrödinger equation
Theodoros Katsaounis, Irene Kyza
We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schrödinger-type equations, in the norm. For the discretization in…