Error estimation and adaptivity for the finite element method in acoustics: 2D and 3D applications

This paper is dedicated to the control of accuracy and to the adaptivity of the finite element simulation of sound propagation. Assuming time-harmonic behaviour, the mathematical models are given as boundary value problems fo r the Helmholtz equation. Two singularities inherent to the operator are de monstrated: the k-singularity, related to the phase shift between the exact and the numerical waves, and the lambda-singularity corresponding to the s ingularity at the eigenfrequencies. Two a posteriori error estimators are developed and the numerical tests sho w that, due to these specific singularities, error control cannot, in gener al, be accomplished by just 'transplanting' methods that work well in stati c computations. Furthermore, for low wave numbers, it is necessary also to control the influence of the geometric or physical singularities. An h-adap tive version with refinement is applied to 2D and 3D real-life problems. (C ) 1999 Elsevier Science B.V. All rights reserved.