On Finite Element Methods for Fully Nonlinear Elliptic Equations and Systems

For the first time, we present for the general case of fully nonlinear elliptic differential equations and systems of order $2$ and $2m$ in ${\text{R}}^n$, a stability and convergence proof for nonstandard finite element, spectral and wavelet methods. We include the necessary quadrature and cubature approximations. Essential tool is a new regularity result for solutions of finite element equations. For this lecture we erstrict the presentation to equations of order two and to FEMs. An important exammple is the Monge-Ampere equation.