Finite Element Methods for Least-Squares Problems

Speaker: Prof. Susanne C, Brenner ，Louisiana State University

Title: Finite Element Methods for Least-Squares Problems

Language: English

Time & Venue: 2024.07.22 09:00-10:00 N204

Abstract: Finite dimensional linear and nonlinear leastsquares problems appear in data fitting and the solution of nonlinear equations. In this talk I will present some recent results for the infinite dimensional analogs of such problems. They include (i) a genera l framework for solving distributed elliptic optimal control problems with pointwise state constraints by finite element methods originally designed for fourth order elliptic boundary value problems, (ii) a multiscale finite element method for solving dist ributed elliptic optimal control problems with rough coefficients and pointwise control constraints, and (iii) a convexity enforcing nonlinear least squares finite element method for solving the Monge Ampere equation.