TY - GEN A1 - Henning, Patrick A1 - Malqvist, Axel A1 - Peterseim, Daniel T1 - A rigorous Multiscale Method for semi-linear elliptic problems N2 - In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coeffcient functions. For this purpose we construct a generalized finite element basis that spans a low dimensional multiscale space. The basis is assembled by performing localized linear finescale computations in small patches that have a diameter of order H |log(H)| where H is the coarse mesh size. Without any assumptions on the type of the oscillations in the coeffcients, we give a rigorous proof for a linear convergence of the H1-error with respect to the coarse mesh size. To solve the arising equations, we propose an algorithm that is based on a damped Newton scheme in the multiscale space. KW - computational homogenization KW - numerical upscaling KW - finite element KW - error analysis Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1176 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11768 ER -