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- W3159607397 abstract "In this thesis, we study the approximation and stabilization of some evolution equations, using semigroup theory and some spectral analysis. This Ph.D. thesis is divided into two main parts. In the first part, as in [3, 4], we consider the approximation of second order evolution equations modeling the vibrations of elastic structures. It is well known that the approximated system by finite elements or finite differences is not uniformly exponentially or polynomially stable with respect to the discretization parameter, even if the continuous system has this property. Therefore, our goal is to damp the spurious high frequency modes by introducing numerical viscosity terms in the approximation scheme. With these viscosity terms, we show the exponential or polynomial decay of the discrete scheme when the continuous problem has such a decay and when the spectrum of the spatial operator associated with the undamped problem satisfies the generalized gap condition. By using the Trotter-Kato Theorem, we further show the convergence of the discrete solution to the continuous one. Some illustrative examples are also presented." @default.
- W3159607397 created "2021-05-10" @default.
- W3159607397 creator A5028326746 @default.
- W3159607397 date "2013-05-27" @default.
- W3159607397 modified "2023-09-23" @default.
- W3159607397 title "Stabilization and approximation of some distributed systems by either dissipative or inde" @default.
- W3159607397 hasPublicationYear "2013" @default.
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