2024/10/24 by Harbir Antil, Sören Bartels, Antil, Harbir +5 · 2 citations
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #Optimization and Variational Analysis #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2410.18780
In this paper, on the basis of a (Fenchel) duality theory on the continuous level, we derive an a posteriori error identity for arbitrary conforming approximations of a primal formulation and a dual formulation of variational problems involving gradient constraints. In addition, on the basis of a (Fenchel) duality theory on the discrete level, we derive an a priori error identity that applies to the approximation of the primal formulation using the Crouzeix-Raviart element and to the approximation of the dual formulation using the Raviart-Thomas element, and leads to error decay rates that are optimal with respect to the regularity of a dual solution.