Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 283-289 |
| Number of pages | 7 |
| Journal | Comptes Rendus Mathematique |
| Volume | 354 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Mar 2016 |
| Externally published | Yes |
Bibliographical note
Funding Information:We would like to thank M. Grepl and M. Kärcher of RWTH Aachen University, and A.T. Patera of MIT for the helpful discussions, comments, and their careful critique of this manuscript. We also thank J.-B. Wahl and C. Prud'homme of Université de Strasbourg for their kind help with the French translation. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through Grant GSC 111 .
Publisher Copyright:
© 2015 Académie des sciences.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
Funding
We would like to thank M. Grepl and M. Kärcher of RWTH Aachen University, and A.T. Patera of MIT for the helpful discussions, comments, and their careful critique of this manuscript. We also thank J.-B. Wahl and C. Prud'homme of Université de Strasbourg for their kind help with the French translation. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through Grant GSC 111 .