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dc.contributor.authorErvedoza, S.
dc.contributor.authorMarica, A.
dc.contributor.authorZuazua, E.
dc.description.abstractWe build nonuniform numerical meshes for the finite difference and finite element approximations of the one-dimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, in the sense that the full discrete energy can be observed by means of boundary measurements, uniformly with respect to the mesh size. The construction of the nonuniform mesh is achieved by means of a concave diffeomorphic transformation of a uniform grid into a nonuniform one, making the mesh finer and finer when approaching the right boundary. For uniform meshes it is known that high-frequency numerical wave packets propagate very slowly without ever getting to the boundary. Our results show that this pathology can be avoided by taking suitable nonuniform meshes. This also allows us to build convergent numerical algorithms for the approximation of boundary controls of the wave equation.
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectboundary control
dc.subjectboundary observation
dc.subjectnonuniform meshes
dc.subjectnumerical approximation
dc.subjectwave equation
dc.titleNumerical meshes ensuring uniform observability of one-dimensional waves: Construction and analysis
dc.journal.titleIMA Journal of Numerical Analysisen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España