Abstract for the talk at 16.06.2005 (15:15 h)

Klaus Böhmer (Philipps-Universität Marburg)

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 , 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.