10 citations · 15 across the 10 of their papers we have counts for
10 papers
A dichotomy of finite element spaces and its application to an energy-conservative scheme for the regularized long wave equation
Dimitrios Antonopoulos, Dimitrios Mitsotakis
Certain energy-conservative Galerkin discretizations for nonlinear dispersive wave equations have revealed an unusual convergence behavior: optimal convergence is attained when con…
Bona-Smith-type systems in bounded domains with slip-wall boundary conditions: Theoretical justification and a conservative numerical scheme
Dimitrios Antonopoulos, Dimitrios Mitsotakis
Considered herein is a class of Boussinesq systems of Bona-Smith type that describe water waves in bounded two-dimensional domains with slip-wall boundary conditions and variable b…
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…
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…
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…
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 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…