Browsing by Author "Marica, A."
Now showing items 18 of 8

Boundary stabilization of numerical approximations of the 1D variable coefficients wave equation: A numerical viscosity approach
Marica, A.; Zuazua, E. (20141231)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 semidiscretizations. It is wellknown ... 
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]
Marica, A.; Zuazua, E. (20111231)We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space semidiscretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in ... 
Localized solutions and filtering mechanisms for the discontinuous Galerkin semidiscretizations of the 1d wave equation [Solutions localisées et mécanismes de filtrage pour les approximations de Galerkin discontinues de l'équation des ondes.]
Marica, A.; Zuazua, E. (20101231)We perform a complete Fourier analysis of the semidiscrete 1d wave equation obtained through a P1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid. The resulting system exhibits ... 
Localized solutions for the finite difference semidiscretization of the wave equation [Solutions localisées pour la semidiscrétisation par différences finies de l'équation des ondes]
Marica, A.; Zuazua, E. (20101231)We study the propagation properties of the solutions of the finite difference space semidiscrete wave equation on a uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that ... 
Numerical meshes ensuring uniform observability of onedimensional waves: Construction and analysis
Ervedoza, S.; Marica, A.; Zuazua, E. (20160101)We build nonuniform numerical meshes for the finite difference and finite element approximations of the onedimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, ... 
On the quadratic finite element approximation of onedimensional waves: Propagation, observation, and control
Marica, A.; Zuazua, E. (20121231)We study the propagation, observation, and control properties of the quadratic P 2classical finite element semidiscretization of the onedimensional wave equation on a bounded interval. A careful Fourier analysis of the ... 
Propagation of 1D Waves in Regular Discrete Heterogeneous Media: A Wigner Measure Approach
Marica, A.; Zuazua, E. (20141231)In this article, we describe the propagation properties of the onedimensional wave and transport equations with variable coefficients semidiscretized in space by finite difference schemes on nonuniform meshes obtained ... 
Symmetric discontinuous Galerkin approximations of waves: high frequency propagation and control
Marica, A.; Zuazua, E. (20141231)This work describes the propagation properties of the socalled symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1d wave equation. This is done by means of linear approximations on uniform ...