The penetration function and its application to microscale problems
The penetration function measures the effect of the boundary data on the energy of the solution of a second order linear elliptic PDE taken over an interior subdomain. Here the coefficients of the PDE are functions of position and often represent the material properties of non homogeneous media with microstructure. The penetration function is used to assess the accuracy of global-local approaches for recovering local solution features from coarse grained solutions such as those delivered by homogenization theory.
penetration function homogenization approximation theory saint venant principle