A slack approach to reduced-basis approximation and error estimation for variational inequalities

We propose a novel approach for computing certified reduced-basis approximations to solutions to variational inequalities of the first kind. The proposed approach has three components: (i) a slack-based approximation for the solution; (ii) a primal approximation for the Lagrange multiplier; and (iii) a posteriori bounds for the error in the combined primal-slack variable approximation. The strict feasibility of the primal-slack approximations leads to two significant improvements upon existing methods. First, it provides a posteriori error bounds that are significantly sharper than existing bounds. Second, it enables a full offline-online computational decomposition, in which the online cost to compute the error bound is completely independent of the dimension of the original (high-dimensional) problem. Our numerical results allow us to compare the performance of the proposed and existing approaches. (c) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.