nlfem: A flexible 2d Fem Code for Nonlocal Convection-Diffusion and Mechanics

TL;DR

nlfem is a versatile finite element code designed for nonlocal models, demonstrated on diffusion and peridynamics, enabling flexible simulations of nonlocal phenomena in 2D.

Contribution

The paper introduces nlfem, a new finite element software for nonlocal models with a solid mathematical foundation and practical demonstrations.

Findings

Successfully applied to nonlocal diffusion models

Demonstrated on 2D bond-based peridynamics

Code is open-source under MIT License

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. The code nlfem is published under the MIT License and can be freely downloaded.