Anna Persson: A generalized finite element method for elasticity

Abstract:

In this talk I will present a generalized finite element method for elasticity equations with highly varying (multiscale) coefficients. Such equations typically occur when modeling the deformation of a heterogeneous medium, for instance a composite material. For these problems, classical polynomial based finite elements fail to approximate the solution well unless the mesh width resolves the data variations. In many applications this leads to issues with computational cost and available memory. To overcome this difficulty new approaches and methods are needed.

The method presented in this talk is based on localized orthogonal decomposition, first introduced by Målqvist and Peterseim (2014). A short review of this method for elliptic problems will be given before I discuss how to apply the ideas to linear elasticity equations. In addition, I will show how the method can be extended to thermoelastic systems describing the deformation of materials exposed to temperature changes.