Summary: Fully anisotropic goal-oriented mesh adaptation for
3D steady Euler equations
, A. Dervieuxb
, F. Alauzeta
aINRIA, Projet Gamma, Domaine de Voluceau, Rocquencourt, BP 105,
78153 Le Chesnay Cedex, France.
bINRIA, Projet Tropics, 2004 route des lucioles - BP 93,
06902 Sophia Antipolis Cedex, France
cGeorge Mason University, Computational Fluid Dynamics Center,
4400 university drive, MS6A2, Fairfax, VA, USA
This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very
well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the
contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions.
Consequently, a full and strong coupling between both is hard to achieve due to this apparent incompatibility. This paper shows
how to achieve this coupling in three steps.
First, a new a priori error estimate is proved in a formal framework adapted to goal-oriented mesh adaptation for output
functionals. This estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error.
Second, the error estimate is applied to the set of steady compressible Euler equations which are solved by a stabilized Galerkin