A posteriori error estimates for Webster's equation in wave propagation
  We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in generalised form has been rigorously derived in a previous article starting from the wave equation, and it approximates cross-sectional averages of the propagating wave. Here, the approximation error is estimated by an a posteriori technique. 
Teemu Lukkari and Jarmo Malinen
math.AP math.DS