Worked Out Problem 2: A Linear Elasticity Problem on a Square

In this chapter, we consider a vector elliptic PDE modeling a parametric linear elasticity problem in a two-dimensional heterogeneous domain. The aim is to obtain efficient evaluations of the vector displacement field and the output of interest, defined as the integrated horizontal displacement over the loaded boundary. The solution is approximated using reduced order modeling techniques based on the POD-Galerkin method. The problem is described by presenting the physical domain, the goal, the parametrization, the boundary conditions, the governing PDE, and the corresponding weak formulation with its affine decomposition. Numerical results show the performance of the reduced approach with respect to the high-fidelity discretization, the quantity of interest, and the speedup. We provide the links to the source code, to the Jupyter notebook, and to the web-server ARGOS.