A finite element method for a two-dimensional Pucci equation - Brenner, Susanne C.; Sung, Li-yeng; Tan, Zhiyu (Comptes Rendus. Mécanique, 2023)
A nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. We obtain a priori and a posteriori error estimates and present corroborating numerical results, where the discrete nonsmooth and nonlinear optimization problems are solved by an active set method and an alternating direction method with multipliers.