Admissible fields and error estimation for acoustic FEA with low wavenumbers

A posteriori error estimation in constitutive law, that has been mainly dev eloped for stress analysis, can be applied to acoustic finite element analy ses with low wavenumbers. The mathematical background is developed and the concept of admissible solutions is defined for the acoustic problem conside ring Dirichlet, Neumann and mixed boundary conditions. Particular attention is devoted to the calculation of the admissible acoustic velocity which mu st be of order p + 1 to satisfy the Helmholtz equation. Numerical analyses with linear triangles show very encouraging results with low wavenumbers, n amely the estimated error converges in O(h(P)), i.e. the same order as the exact error, and the distribution of the exact error is particularly well e stimated, i.e. the areas containing concentrations of error are correctly i dentified but locally overestimated. Moreover, the estimated global absolut e error always overestimates the exact error. (C) 1999 Civil-Comp Ltd and E lsevier Science Ltd. All rights reserved.