Generalized p-FEM in homogenization

Homogenization via p-FEM for Problems

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...

The Role of Numerical Integration in Numerical Homogenization

Finite elements methods (FEMs) with numerical integration play a central role in numerical homogenization methods for partial differential equations with multiple scales, as the effective data in a homogenization problem can only be recovered from a microscopic solver at a finite number of points in the computational domain. In a multiscale framework the convergence of a FEM with numerical inte...

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...

Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization

We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L norm. We then derive optimal a priori error estimates in the H and L norm for a FEM with variational crimes due to numerical integration. As an application we d...