Displaying similar documents to “Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes”

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...

A uniformly controllable and implicit scheme for the 1-D wave equation

Arnaud Münch (2005)

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

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This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters h and Δ t . We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order h 2 and...

A new conservative finite difference scheme for Boussinesq paradigm equation

Natalia Kolkovska, Milena Dimova (2012)

Open Mathematics

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A family of nonlinear conservative finite difference schemes for the multidimensional Boussinesq Paradigm Equation is considered. A second order of convergence and a preservation of the discrete energy for this approach are proved. Existence and boundedness of the discrete solution on an appropriate time interval are established. The schemes have been numerically tested on the models of the propagation of a soliton and the interaction of two solitons. The numerical experiments demonstrate...

Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction

Abdur Rashid, Shakaib Akram (2010)

Applications of Mathematics

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In this paper, the evolution equations with nonlinear term describing the resonance interaction between the long wave and the short wave are studied. The semi-discrete and fully discrete Crank-Nicholson Fourier spectral schemes are given. An energy estimation method is used to obtain error estimates for the approximate solutions. The numerical results obtained are compared with exact solution and found to be in good agreement.

Convergence of a two-grid algorithm for the control of the wave equation

Liviu Ignat, Enrique Zuazua (2009)

Journal of the European Mathematical Society

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We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d wave equation in the square. We prove the uniform (with respect to the meshsize) boundary observability for the solutions obtained by the two-grid preconditioner introduced by Glowinski [9]. Our method uses previously known uniform observability inequalities for low frequency solutions and a dyadic spectral time decomposition. As a consequence we prove the convergence of the...