Displaying similar documents to “Uniformly exponentially or polynomially stable approximations for second order evolution equations and some applications”

Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations

Noel J. Walkington (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.

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...

Uniformly exponentially stable approximations for a class of second order evolution equations

Karim Ramdani, Takéo Takahashi, Marius Tucsnak (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the approximation of a class of exponentially stable infinite dimensional linear systems modelling the damped vibrations of one dimensional vibrating systems or of square plates. It is by now well known that the approximating systems obtained by usual finite element or finite difference are not, in general, uniformly stable with respect to the discretization parameter. Our main result shows that, by adding a suitable numerical viscosity term in the numerical scheme, our...