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Multi-methodological approaches combining quantum-mechanical and/or atomistic simulations
with continuum methods have become increasingly important when addressing multi-scale phenomena in
computational materials science. A crucial aspect when applying these strategies is to carefully check,
and if possible to control, a variety of intrinsic errors and their propagation through a particular multimethodological
scheme. The first part of our paper critically reviews a few selected sources of errors
frequently occurring in quantum-mechanical approaches to materials science and their multi-scale propagation
when describing properties of multi-component and multi-phase polycrystalline metallic alloys.
Our analysis is illustrated in particular on the determination of i) thermodynamic materials properties at
finite temperatures and ii) integral elastic responses. The second part addresses methodological challenges
emerging at interfaces between electronic structure and/or atomistic modeling on the one side and selected
continuum methods, such as crystal elasticity and crystal plasticity finite element method (CEFEM and
CPFEM), new fast Fourier transforms (FFT) approach, and phase-field modeling, on the other side.