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A Posteriori Error Estimates and a Local Refinement Strategy for a Finite Element Method to Solve Structural-Acoustic Vibration Problems

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Abstract

This paper deals with an adaptive technique to compute structural-acoustic vibration modes. It is based on an a posteriori error estimator for a finite element method free of spurious or circulation nonzero-frequency modes. The estimator is shown to be equivalent, up to higher order terms, to the approximate eigenfunction error, measured in a useful norm; moreover, the equivalence constants are independent of the corresponding eigenvalue, the physical parameters, and the mesh size. This a posteriori error estimator yields global upper and local lower bounds for the error and, thus, it may be used to design adaptive algorithms. We propose a local refinement strategy based on this estimator and present a numerical test to assess the efficiency of this technique.

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 172, 1900 La Plata, Argentina

    Ana Alonso & Anahí Dello Russo

  2. Centro Atómico Bariloche, 8400 Bariloche, Río Negro, Argentina

    Claudio Padra

  3. Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Rodolfo Rodríguez

Authors
  1. Ana Alonso
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  2. Anahí Dello Russo
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  3. Claudio Padra
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  4. Rodolfo Rodríguez
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Correspondence to Rodolfo Rodríguez.

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Alonso, A., Russo, A.D., Padra, C. et al. A Posteriori Error Estimates and a Local Refinement Strategy for a Finite Element Method to Solve Structural-Acoustic Vibration Problems. Advances in Computational Mathematics 15, 25–59 (2001). https://doi.org/10.1023/A:1014243118190

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