106 citations · 162 across the 15 of their papers we have counts for
17 papers
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…
Axisymmetric flows with swirl for Euler and Navier-Stokes equations
Theodoros Katsaounis, Ioanna Mousikou, Athanasios E. Tzavaras
We consider the incompressible axisymmetric Navier-Stokes equations with swirl as an idealized model for tornado-like flows. Assuming an infinite vortex line which interacts with a…
Self-similar axisymmetric flows with swirl
Theodoros Katsaounis, Ioanna Mousikou, Athanasios E. Tzavaras
We consider an infinite vortex line in a fluid which interacts with a boundary surface as a simplified model for tornadoes. We study self-similar solutions for stationary axisymmet…
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…
Localization in adiabatic shear flow via geometric theory of singular perturbations
Min-Gi Lee, Theodoros Katsaounis, Athanasios Tzavaras
We study localization occurring during high speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition am…
Localization in inelastic rate dependent shearing deformations
Theodoros Katsaounis, Min-Gi Lee, Athanasios Tzavaras
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into…
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…
Emergence of coherent localized structures in shear deformations of temperature dependent fluids
Theodoros Katsaounis, Julien Olivier, Athanasios E. Tzavaras
Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadam…
Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza
Semiclassical asymptotics for linear Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of att…
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…
Finite volume schemes for Boussinesq type equations
Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive wa…
Dispersive wave runup on non-uniform shores
Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis
Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of su…
Finite volume schemes for dispersive wave propagation and runup
Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive wa…