Mathematikgebäude, Raum M 511

C0 interior penalty Galerkin (C0IPG) methods for fourth order elliptic problems benefits from simple standard Lagrange finite element spaces which are also used for second order problems. Although a posteriori estimators are available in the literature, due to the non-conformity of the ansatz spaces, a rigorose convergence analysis of adaptive C0IPG methods for elliptic fourth order problems appears to be difficult. In this talk we present a first convergence analysis for adaptive C0IPG methods for the biharmonic problem which provides convergence without rates. Based on ideas in a recent result from Kreuzer and Georgoulis the theory is accomplished by using a quasi interpolation which takes into account the future refinements and a new limit space of the adaptively created non-conforming discrete spaces.

M.Sc. Alexander Dominicus

TU Dortmund