In many applications the quantities of interest are a series of
target functionals of the solution to the governing system of
partial differential equations rather than the solution itself. For
example, in the field of aerodynamics, examples include the drag and
lift coefficients of an airfoil immersed into a fluid, the pressure
difference between the leading and trailing edges of the airfoil and
point evaluations of the density or pressure on the profile of the
airfoil. While traditionally these quantities are measured in wind
tunnel experiments, nowadays these experiments are increasingly
replaced by numerical simulations aiming to predict these quantities
to a high level of accuracy.
In a series of previous articles, we have developed the theory of
goal--oriented a posteriori error estimation for
discontinuous Galerkin methods applied to inviscid compressible
fluid flows. On the basis of Type I a posteriori bounds we
considered the design of adaptive finite element algorithms that are
capable of generating optimal meshes specifically tailored to the
efficient computation of a single target functional of
practical interest. The purpose of the current article is to extend
this earlier work to the case when several target
functionals of the solution need to be simultaneously approximated
to a given level of accuracy.