In this paper we present two different kinds of error estimators for acoustic problems: a residual-based and a dual weighted residual one. The former error estimator is explicit and cheap to compute. The latter is based on a duality argument and it is capable of computing accurate and reliable estimations of quantities of interest, which can be safely used for finite element analysis and model validation. The error estimators presented in this work are designed to work with a \(hp\)-adaptive discontinuous Galerkin methods.
Giani, S. (2013). High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems. Computing, 95(1 Supplement), S215-S234. https://doi.org/10.1007/s00607-012-0253-5