This talk introduces finite element methods for a class of elliptic fully nonlinear partial
differential equations. They are based on a minimal residual principle that builds upon
the Alexandrov–Bakelman–Pucci estimate. Under rather general structural assumptions on
the operator, convergence of C1 conforming and discontinuous Galerkin methods is proven in
the L∞ norm. Numerical experiments on the performance of adaptive mesh refinement driven
by local information of the residual in two and three space dimensions are provided.
(joint work with Ngoc Tien Tran)