320 IGPM320.pdf        January 2011
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