Error analysis of HDG approximations for elliptic variational inequality: obstacle problem

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Abstract

In this article, we study the HDG approximation for the obstacle problem, i.e., variational inequalities, with remarkable convergence properties. Using polynomials of degree k ≥ 0 for both the potential u and the flux q, we show that the approximations of the potential and flux converge in L2 with the optimal order of k + 1 . The approximate trace of the potential is proved to converge with optimal order k + 1 in L2. Finally, numerical results are presented to verify these theoretical results.

Keywords

HDG Error analysis Elliptic variational inequality 

Mathematics Subject Classification (2010)

65F10 65N30 65N55 

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Notes

Funding information

This subject is supported partially by NSFC No. 11672032.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Institute of TechnologyBeijingChina

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