320	RWTH Publication No: 47317        2011        IGPM320.pdf
TITLE	The AL Basis for the Solution of Elliptic Problems in Heterogeneous Media
AUTHORS	Lars Grasedyck, Isabelle Greff, Stefan Sauter
ABSTRACT	In this paper, we will show that, for elliptic problems in heterogeneous media, there exists a local (generalized) finite element basis (AL basis) consisting of O((log 1/h)d+1 basis functions per nodal point such that the convergence rates of the classical finite element method for Poisson-type problems are preserved. We provide several numerical examples beyond our theory, where even O(1) basis functions per nodal point are sufficient to preserve the convergence rates.
KEYWORDS	Elliptic problem, heterogeneous media, Green’s function, generalized finite elements
DOI	10.1137/11082138X
PUBLICATION	SIAM Journal Multiscale Modeling and Simulation, 10,1, 245-258, 2012