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The penetration function and its application to microscale problems |
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| Authors: | Ivo Babuška Robert Lipton Michael Stuebner |
| Affiliation: | (1) ICES and Department of Aerospace Engineering, University of Texas, Austin, TX 78712, USA;(2) Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA;(3) Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA |
| Abstract: | 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. AMS subject classification (2000) 65N15, 78M40 |
| Keywords: | penetration function approximation theory homogenization Saint Venant principle |
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