Search
Now showing items 1-8 of 8
Numerical meshes ensuring uniform observability of one-dimensional waves: Construction and analysis
(2016-01-01)
We build nonuniform numerical meshes for the finite difference and finite element approximations of the one-dimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, ...
Symmetric discontinuous Galerkin approximations of waves: high frequency propagation and control
(2014-12-31)
This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform ...
Propagation of 1D Waves in Regular Discrete Heterogeneous Media: A Wigner Measure Approach
(2014-12-31)
In this article, we describe the propagation properties of the one-dimensional wave and transport equations with variable coefficients semi-discretized in space by finite difference schemes on non-uniform meshes obtained ...
Boundary stabilization of numerical approximations of the 1-D variable coefficients wave equation: A numerical viscosity approach
(2014-12-31)
In this paper, we consider the boundary stabilization problem associated to the 1- d wave equation with both variable density and diffusion coefficients and to its finite difference semi-discretizations. It is well-known ...
On the quadratic finite element approximation of one-dimensional waves: Propagation, observation, and control
(2012-12-31)
We study the propagation, observation, and control properties of the quadratic P 2-classical finite element semidiscretization of the one-dimensional wave equation on a bounded interval. A careful Fourier analysis of the ...
High frequency wave packets for the Schrödinger equation and its numerical approximations [Paquets d'ondes à haute fréquence pour l'équation de Schrödinger et ses approximations numériques]
(2011-12-31)
We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in ...
Localized solutions for the finite difference semi-discretization of the wave equation [Solutions localisées pour la semi-discrétisation par différences finies de l'équation des ondes]
(2010-12-31)
We study the propagation properties of the solutions of the finite difference space semi-discrete wave equation on a uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that ...
Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation [Solutions localisées et mécanismes de filtrage pour les approximations de Galerkin discontinues de l'équation des ondes.]
(2010-12-31)
We perform a complete Fourier analysis of the semi-discrete 1-d wave equation obtained through a P1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid. The resulting system exhibits ...