Goal-Oriented A Posteriori Error Estimation for Compressible Fluid Flows

R. Hartmann and P. Houston

Abstract:

We consider so-called `goal-oriented' a posteriori error estimation for discontinuous Galerkin finite element approximations to the compressible Euler equations of gas dynamics. By employing a hyperbolic duality argument, we derive weighted, or Type I, a posteriori error estimates which bound the error measured in terms of certain target functionals of real or physical interest. The practical advantages of this general approach are illustrated by a series of numerical experiments.