A Duality Approach to Error Estimation for Variational Inequalities
For researchers in contact mechanics and reduced basis methods, this provides a more efficient and accurate error estimation technique for variational inequalities.
The paper introduces a duality approach for computing approximations and sharp a posteriori error bounds for variational inequalities, improving upon existing reduced basis methods by achieving error bounds that match the convergence rate and enabling a fully offline-online decomposition with online cost independent of the original problem dimension. Numerical results demonstrate superiority for high-dimensional problems.
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon existing methods introduced in the context of the reduced basis method in two ways. First, it provides sharp a posteriori error bounds which mimic the rate of convergence of the RB approximation. Second, it enables a full offline-online computational decomposition in which the online cost is completely independent of the dimension of the original (high-dimensional) problem. Numerical results comparing the performance of the proposed and existing approaches illustrate the superiority of the duality approach in cases where the dimension of the full problem is high.