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In this work, we further develop multigoal-oriented a posteriori errorestimation for the nonlinear, stationary, incompressible Navier-Stokesequations. It is an extension of our previous work [B. Endtmayer, U. Langer, T.Wick: Two-side a posteriori error estimates for the DWR method, $SISC$, 2019,accepted]. We now focus on $h$ mesh refinement and $p$ enrichment for the errorestimator. These advancements are demonstrated with the help of a numericalexample

Hierarchical DWR Error Estimates for the Navier Stokes Equation: $h$ and $p$ Enrichment