Flux Reconstruction for Goal-Oriented A Posteriori Error Estimation
This work provides a practical error estimation tool for finite element computations, particularly useful for engineers and scientists needing reliable adaptive mesh refinement.
The paper proposes a new heuristic goal-oriented a posteriori error estimator combining dual weighted residual and equilibrated methods, demonstrating practical reliability and optimally convergent adaptivity on singular domains and coarse meshes.
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the error estimator, confirming theoretical predictions, as well as optimally convergent adaptivity even over singular domains and coarse meshes. The central algorithm is a localized flux reconstruction, which has been implemented in the finite element library deal.II. For a solid preparation we assess the performance of the equilibrated a posteriori error estimator of the energy norm in numerical experiments. Moreover, we give what seems to be first rigorous discussion in the numerical literature of localized flux reconstruction over quadrilateral meshes with hanging nodes.