Mathematics Colloquium: Gradient Constrained Variational Problems: A Priori and A Posteriori Error Identities

Speaker:  Rohit Khandelwal, GMU

Title: Gradient Constrained Variational Problems: A Priori and A Posteriori Error Identities 

Abstract: Nonsmooth variational problems are ubiquitous in science and engineering, for e.g., fracture modeling and contact mechanics. This talk presents a generic primal-dual framework to tackle these types of nonsmooth problems. Special attention is given to variational problems with gradient constraints. The key challenge here is how to project onto the constraint set both at the continuous and discrete levels. In fact, both a priori and a posteriori error analysis for such nonsmooth problems has remained open. In this talk, on the basis of a (Fenchel) duality theory at the continuous level, an a posteriori error identity for arbitrary conforming approximations of primal-dual formulations is derived. In addition, on the basis of a (Fenchel) duality theory at the discrete level, an a priori error identity for primal (Crouzeix–Raviart) and dual (Raviart–Thomas) formulations is established. The talk concludes by deriving the optimal a priori error decay rates.

Time:  Friday, April 4, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person