Prof Ed Bueler (University of Alaska Fairbanks): Introduction to variational inequalities and their finite element solution
Lectures will be held on Tuesdays: 20 Oct, 27 Oct, 3 Nov, 17 Nov, at 15:00.
Abstract: This four-lecture series introduces variational inequalities to a general applied mathematical audience, pursues their finite element solution, and applies them to a geophysical problem. Variational inequalities are partial differential equation weak forms, but subject to bounds on their solution(s). They reformulate how one might pose boundary conditions at a free location; where the conditions apply is now determined simultaneously along with the solution. Certain variational inequalities state the KKT conditions of optimization problems in function spaces, and in all cases these continuum models introduce admissibility and complementarity concerns into numerical solver methodology. Examples of variational inequalities include the classical obstacle problem, the problem of elastic contact, and, as I will emphasize, the problem of finding the extent of glaciation in a time- and space-varying climate. Recent results and open problems will appear, regarding multigrid approaches, adaptive mesh refinement, higher-order elements, and well-posedness of the glacier model.