10 citations · 28 across the 19 of their papers we have counts for
19 papers
Notes on the Boussinesq-Full dispersion systems for internal waves: Numerical solution and solitary waves
V. A. Dougalis, A. Durán, L. Saridaki
In this paper we study some theoretical and numerical issues of the Boussinesq/Full dispersion system. This is a a three-parameter system of pde's that models the propagation of in…
On the well-posedness of the Galerkin semidiscretization of the periodic initial-value problem of the Serre equations
D. C. Antonopoulos, V. A. Dougalis, D. E. Mitsotakis
We consider the periodic initial-value problem for the Serre equations of water-wave theory and its semidiscrete approximation in the space of smooth periodic polynomial splines. W…
Numerical solution of internal-wave systems in the intermediate long wave and the Benjamin-Ono regimes
Vassilios A. Dougalis, Angel Durán, Leetha Saridaki
The paper is concerned with the numerical approximation of the Intermediate Long Wave and Benjamin-Ono systems, that serve as models for the propagation of interfacial internal wav…
Notes on numerical analysis and solitary wave solutions of Boussinesq/Boussinesq systems for internal waves
V. A. Dougalis, A. Duran, L. Saridaki
In this paper a three-parameter family of Boussinesq systems is studied. The systems have been proposed as models of the propagation of long internal waves along the interface of a…
Galerkin finite element methods for the numerical solution of two classical-Boussinesq type systems over variable bottom topography
G. Kounadis, D. C. Antonopoulos, V. A. Dougalis
We consider two `Classical' Boussinesq type systems modelling two-way propagation of long surface waves in a finite channel with variable bottom topography. Both systems are derive…
Notes on a high order fully discrete scheme for the Korteweg-de vries equation with a time-stepping procedure of Runge-Kutta-composition type
Vassilios A. Dougalis, Angel Durán
We consider the periodic initial-value problem for the Korteweg-de Vries equation that we discretize in space by a spectral Fourier-Galerkin method and in time by an implicit, high…
Galerkin finite element methods for the Shallow Water equations over variable bottom
G. Kounadis, V. A. Dougalis
We consider the one-dimensional shallow water equations (SW) in a finite channel with variable bottom topography. We pose several initial-boundary-value problems for the SW system,…
On the standard Galerkin method with explicit RK4 time stepping for the Shallow Water equations
D. c. Antonopoulos, V. a. Dougalis, G. Kounadis
We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension. We discretize the problem in space by the standard Galerkin finite eleme…
On error estimates for Galerkin finite element methods for the Camassa-Holm equation
D. C. Antonopoulos, V. A. Dougalis, D. E. Mitsotakis
We consider the Camassa-Holm (CH) equation, a nonlinear dispersive wave equation that models one-way propagation of long waves of moderately small amplitude. We discretize in space…
Semidiscrete approximation to Benjamin-type equations
Vassilios A. Dougalis, Angel Duran
In this paper a semidiscrete Fourier pseudospectral method for approximating Benjamin-type equations is introduced and analyzed. A study of convergence is presented.
Numerical approximation to Benjamin type equations. Generation and stability of solitary waves
Vassilios A. Dougalis, Angel Duran, Dimitrios Mitsotakis
This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The num…
Error estimates for Galerkin approximations of the Serre equations
Dimitrios Antonopoulos, Vassilios Dougalis, Dimitrios Mitsotakis
We consider the Serre system of equations which is a nonlinear dispersive system that models two-way propagation of long waves of not necessarily small amplitude on the surface of…
Notes on Galerkin-finite element methods for the Shallow Water equations with characteristic boundary conditions
D. C. Antonopoulos, V. A. Dougalis
We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions…
Notes on error estimates for the standard Galerkin-finite element method for the Shallow Water equations
D. C. Antonopoulos, V. A. Dougalis
We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension, and also the analogous problem for a symmetric variant of the system. As…
Notes on the numerical solution of the Benjamin equation
V. A. Dougalis, A. Duran, D. Mitsotakis
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of tw…
A Finite Difference method for the Wide-Angle `Parabolic' equation in a waveguide with downsloping bottom
D. C. Antonopoulou, V. A. Dougalis, G. E. Zouraris
We consider the third-order wide-angle `parabolic' equation of underwater acoustics in a cylindrically symmetric fluid medium over a bottom of range-dependent bathymetry. It is kno…
Notes on error estimates for Galerkin approximations of the 'classical' Boussinesq system and related hyperbolic problems
D. C. Antonopoulos, V. A. Dougalis
We consider the `classical' Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small…
Boussinesq Systems of Bona-Smith Type on Plane Domains: Theory and Numerical Analysis
Vassilios Dougalis, Dimitrios Mitsotakis, Jean-Claude Saut
We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions approximating surface wave flows modelled by the three-dimensional Euler equations. We show tha…
Galerkin Methods for Parabolic and SCHR{Ö}DINGER Equations with Dynamical Boundary Conditions and Applications to Underwater Acoustics
D. C. Antonopoulou, V. A. Dougalis, G. E. Zouraris
In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schrödinger evo…