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

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.