Higher-Order Homogenization of Initial/Boundary-Value Problem
Jacob Fish, Wen Chen · Journal of Engineering Mechanics · 2001
Higher-order homogenization of an initial/boundary-value problem with oscillatory coefficients in one dimension is studied. Validity range and limitations of the theory are established. We show that the higher terms are necessary to account for wave dispersion but introduce secular terms that grow unbounded in time. Numerical procedures requiring superconvergent recovery of higher-order derivatives are described.