nlfem: a Flexible 2d FEM Python Code for Nonlocal Convection-Diffusion and Mechanics

Abstract

In this work, we present the mathematical foundation of an assembly code for finite element approximations of nonlocal models with compactly supported, weakly singular kernels. We demonstrate the code on a nonlocal diffusion model in various configurations and on a two-dimensional bond-based peridynamics model. Further examples can be found in D’Elia et al. (Math Models Methods Appl Sci 31(08):1505–1567, 2021). The code nlfem is published under the GNU General Public License (for details, see, e.g., https://www.gnu.org/licenses/gpl-3.0.de.html) and can be freely downloaded at https://gitlab.uni-trier.de/pde-opt/nonlocal-models/nlfem.