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

Abstract

In this work, we further develop multigoal-oriented a posteriori error estimation for the nonlinear, stationary, incompressible Navier-Stokes equations. 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 error estimator. These advancements are demonstrated with the help of a numerical example

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• Efficient and scalable data structures and algorithms for goal-oriented adaptivity of space-time FEM codes