Generalized p-FEM in homogenization

Generalized p-FEM in homogenization

A new nite element method for elliptic problems with locally periodic microstructure of length " > 0 is developed and analyzed. It is shown that the method converges, as " ! 0, to the solution of the homogenized problem with optimal order in " and exponentially in the number of degrees of freedom independent of " > 0. The computational work of the method is bounded independently of ". Numerical...

Homogenization via p-FEM for Problems

Two-Scale FEM for Homogenization Problems

The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale ε " 1 is analyzed. Full elliptic regularity independent of ε is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the ε scale of the solution with work independent of ε and without ana...

Sparse Two-Scale FEM for Homogenization Problems

We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale ε 1. Based on a refined two-scale regularity on the solutions, two-scale tensor product FE spaces are introduced and error estimates which are robust (i.e. independent of ε) are given. We show that under additional two-scale regularity ...

A FEM Multiscale Homogenization Procedure using Nanoindentation for High Performance Concrete

This paper aims to develop a numerical multiscale homogenization method for prediction of elasto-viscoplastic properties of a high performance concrete (HPC). The homogenization procedure is separated into two-levels according to the microstructure of the HPC: the mortar or matrix level and the concrete level. The elasto-viscoplastic behavior of individual microstructural phases of the matrix a...