Multi-scale Modeling Error Of The Linear Elasticity Equations Estimated

In solving the properties of multiple scales contain problem, we usually con-struct macro equation. To construct the macro equation in local area, we need tosolve micro equation. To add artificial boundary conditions in local problem willmanufacturing model error in the solution of macro equation and micro equation.In this paper, we provide a detailed estimate for the modeling error of linear elas-ticity problems with highly oscillatory coefficients. Five different boundary condi-tions are considered: uniform displacement boundary condition, uniform tractionboundary condition, uniform displacement-traction boundary condition, periodicboundary condition, displacement-periodic boundary condition. Our analysis re-veals that all the modeling errors come to the ratio of the small scaleεand thesize of the local domainδ.