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Displaying 1121 –
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We consider the numerical solution, in two- and three-dimensional
bounded domains, of the inverse problem for identifying the location
of small-volume, conductivity imperfections in a medium with homogeneous
background. A dynamic approach, based on the wave equation, permits
us to treat the important case of “limited-view” data. Our numerical
algorithm is based on the coupling of a finite element solution of
the wave equation, an exact controllability method and finally a Fourier
inversion for...
A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate...
It is rather classical to model multiperforated plates by approximate impedance boundary
conditions. In this article we would like to compare an instance of such boundary
conditions obtained through a matched asymptotic expansions technique to direct numerical
computations based on a boundary element formulation in the case of linear acoustic.
This paper presents two observability inequalities for the heat equation over . In the first one, the observation is from a subset of positive measure in , while in the second, the observation is from a subset of positive surface measure on . It also proves the Lebeau-Robbiano spectral inequality when is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.
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, Numer. Math.102 (2006) 413–462] to nonuniform meshes. Our results...
In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in . Lastly, we study the behaviour of this solution and its stability properties with...
In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet
boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence
of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific
properties of bounded sequences in L∞. Lastly, we study the behaviour of this solution and its stability properties...
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