Multiscale Techniques in Linear Elasticity

Abstract

We use a local orthogonal decomposition (LOD) technique to derive a finite element method for planar linear elasticity problems with strongly heterogeneous material data and inhomogeneous Dirichlet and Neumann boundary conditions. These problems are becoming more and more relevant due to the increasing use of composite materials. We apply our generalized finite element method in numerical experiments and observe optimal convergence rates in the energy norm. We also prove an a posteriori error estimate for the method and use it to propose a basic adaptive algorithm for error reduction. Keywords: finite element method, multiscale method, LOD, mixed boundary conditions, a posteriori error estimate, linear elasticity, composite material.