Displaying similar documents to “A uniformly controllable and implicit scheme for the 1-D wave equation”

Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes

Sylvain Ervedoza (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus extending the work [Castro and Micu, (2006) 413–462] to nonuniform meshes....

Boundary controllability of the finite-difference space semi-discretizations of the beam equation

Liliana León, Enrique Zuazua (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...

Uniform stabilization of a viscous numerical approximation for a locally damped wave equation

Arnaud Münch, Ademir Fernando Pazoto (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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This work is devoted to the analysis of a viscous finite-difference space semi-discretization of a locally damped wave equation in a regular 2-D domain. The damping term is supported in a suitable subset of the domain, so that the energy of solutions of the damped continuous wave equation decays exponentially to zero as time goes to infinity. Using discrete multiplier techniques, we prove that adding a suitable vanishing numerical viscosity term leads to a uniform (with respect to the...