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

TL;DR

This paper advances multigoal-oriented a posteriori error estimation for the Navier-Stokes equations by incorporating $h$ mesh refinement and $p$ enrichment, demonstrated through numerical examples.

Contribution

It extends previous work by integrating $h$ and $p$ enrichment strategies into the error estimator for improved accuracy.

Findings

Effective $h$ refinement improves local error control.

$p$ enrichment enhances the estimator's precision.

Numerical examples validate the proposed methods.

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