Work

Variational problems with gradient constraints: A priori and a posteriori error identities

Year: 2025

Type: article

Abstract: 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.

Source: Mathematics of Computation

DOI: 10.1090/mcom/4146

Authors: Harbir Antil, Sören Bartels, Alex Kaltenbach, Rohit Khandelwal

Institutions: George Mason University, University of Freiburg, Technische Universität Berlin, South Asian University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Office of Naval Research, Air Force Office of Scientific Research