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Finite element approximation of spectral acoustic problems on curved domains

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Summary

This paper deals with the finite element approximation of the displacement formulation of the spectral acoustic problem on a curved non convex two-dimensional domain Ω. Convergence and error estimates are proved for Raviart-Thomas elements on a discrete polygonal domain Ω h Ω in the framework of the abstract spectral approximation theory. Similar results have been previously proved only for polygonal domains. Numerical tests confirming the theoretical results are reported.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile

    Erwin Hernández

  2. GI2 MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Rodolfo Rodríguez

Authors
  1. Erwin Hernández
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  2. Rodolfo Rodríguez
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Correspondence to Rodolfo Rodríguez.

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Mathematics Subject Classification (2000):65N25, 65N30, 70J30

Supported by FONDECYT 2000114 (Chile)

Supported by FONDAP in Applied Mathematics (Chile)

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Hernández, E., Rodríguez, R. Finite element approximation of spectral acoustic problems on curved domains. Numer. Math. 97, 131–158 (2004). https://doi.org/10.1007/s00211-003-0501-x

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  • DOI: https://doi.org/10.1007/s00211-003-0501-x

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