Current technological challenges in materials science and high-tech device industry require the solution of boundary
value problems (BVPs) involving regions of various scales, e.g. multiple thin layers, fibre-reinforced composites, and
nano/micro pores. In most cases straightforward application of standard variational techniques to BVPs of practical
relevance necessarily leads to unsatisfactorily ill-conditioned analytical and/or numerical results. To remedy the
computational challenges associated with sub-sectional heterogeneities various sophisticated homogenization techniques
need to be employed. Homogenization refers to the systematic process of smoothing out the sub-structural
heterogeneities, leading to the determination of effective constitutive coefficients. Ordinarily, homogenization involves a
sophisticated averaging and asymptotic order analysis to obtain solutions. In the majority of the cases only zero-order
terms are constructed due to the complexity of the processes involved. In this paper we propose a constructive scheme
for obtaining homogenized solutions involving higher order terms, and thus, guaranteeing higher accuracy and greater
robustness of the numerical results. We present
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