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A posteriori error estimates and a local refinement strategy for a finite element method to solve structural-acoustic vibration problems. (English) Zbl 1043.74041

Summary: 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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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