Abstract
Given an accurate piecewise constant flux approximation $q$ of a smooth (but unknown) exact flux $p$, how can one compute a Sobolev norm of $p$ over a small domain $\omega$? This question arises in a duality argument of goal-oriented finite element a posteriori error analysis. Two equivalent practical estimators $\eta_{M}$ and $\eta_{\mathcal{E}}$ are presented for an approximation $\!q\!$ of $|p|_{H^1(\omega)}$ and model situations are addressed where $\!q\!$ is asymptotically an upper and +lower bound of $|p|_{H^1(\Omega)}$.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
