Numerical Investigations of an Error Bound for Reduced Basis Approximations of Noncoercice Variational Inequalities

We consider variational inequalities with different trial and test spaces and a possibly noncoercive bilinear form. Well-posedness has been shown under general conditions that are e.g. valid for the space-time formulation of parabolic variational inequalities. Fine discretizations for such problems resolve in large scale problems and thus in long computing times. To reduce the size of these problems, we use the Reduced Basis Method (RBM). Combining the RBM with the space-time formulation, a residual based error estimator has been derived in [Glas and Urban (2014)]. In this paper, we provide corresponding numerical results for a parametrized heat inequality model. Particularly, we perform two experiments concerning the error estimator. In the first one, we focus on rigor and efficiency of the error estimator depending on the specific method used for the basis generation and on the shape of the obstacle. In the second one, we show the quantitative reduction using the RBM in this setting. (C) 2015, IFAC (International federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.