Periodic unfolding for lattice structures

Abstract

AbstractThis paper deals with the periodic unfolding for sequences defined on one dimensional lattices in $${\mathbb {R}}^N$$ R N . In order to transfer the known results of the periodic unfolding in $${\mathbb {R}}^N$$ R N to lattices, the investigation of functions defined as interpolation on lattice nodes play the main role. The asymptotic behavior for sequences defined on periodic lattices with information until the first and until the second order derivatives are shown. In the end, a direct application of the results is given by homogenizing a 4th order Dirichlet problem defined on a periodic lattice.