A residual a posteriori error estimator for the finite element solution of the Helmholtz equation Original Research Article

This paper suggests an expression of a residual-based a posteriori error estimation for a Galerkin finite element discretisation of the Helmholtz operator applied in acoustics. In the first part, we summarise the finite element approach and the a priori estimates. The new residual estimator is then formulated, illustrated and tested on two one-dimensional model problems with closed form solution.