Admissible fields and error estimation for acoustic FEA with low wavenumbers
A posteriori error estimation in constitutive law, that has been mainly developed for stress analysis, can be applied to acoustic finite element analyses with low wavenumbers. The mathematical background is developed and the concept of admissible solutions is defined for the acoustic problem considering Dirichlet, Neumann and mixed boundary conditions. Particular attention is devoted to the calculation of the admissible acoustic velocity which must be of order p+1 to satisfy the Helmholtz equation. Numerical analyses with linear triangles show very encouraging results with low wavenumbers, namely the estimated error converges in O(hp), i.e. the same order as the exact error, and the distribution of the exact error is particularly well estimated, i.e. the areas containing concentrations of error are correctly identified but locally overestimated. Moreover, the estimated global absolute error always overestimates the exact error.
admissible fields error estimation acoustics finite element method