English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We perform a posteriori error analysis in the supremum norm for the quadraticdiscontinuous Galerkin method for the elliptic obstacle problem. We define twodiscrete sets (motivated by Gaddam, Gudi and Kamana [1]), one set havingintegral constraints and other one with the nodal constraints at the quadraturepoints, and discuss the pointwise reliability and efficiency of the proposed aposteriori error estimator. In the analysis, we employ a linear averagingfunction to transfer DG finite element space to standard conforming finiteelement space and exploit the sharp bounds on the Green's function of thePoisson's problem. Moreover, the upper and the lower barrier functionscorresponding to continuous solution u are constructed by modifying theconforming part of the discrete solution uh appropriately. Finally, numericalexperiments are presented to complement the theoretical results.

Supremum-norm a posteriori error control of quadratic discontinuous Galerkin methods for the obstacle problem