On finite element methods for fully nonlinear elliptic equations of second order. (English) Zbl 1166.35322

Böhmer, Klaus

SIAM J. Numer. Anal. 46, No. 3, 1212-1249 (2008).

MSC:

35J20	Variational methods for second-order elliptic equations
35J25	Boundary value problems for second-order elliptic equations
35J60	Nonlinear elliptic equations
35J65	Nonlinear boundary value problems for linear elliptic equations
41A15	Spline approximation
46N40	Applications of functional analysis in numerical analysis
47N40	Applications of operator theory in numerical analysis
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry
65H10	Numerical computation of solutions to systems of equations
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N22	Numerical solution of discretized equations for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

conforming; nonconforming finite element method; \({\mathbb R}^n\); variational crimes; fully nonlinear elliptic differential equations; order \(2; C^1\) finite elements; quasi-linear elliptic equations not in divergence form; stability; convergence; regularity for finite element solutions; discrete Newton method; locally quadratic convergence