Comparison of non-matching techniques for the finite element approximation of interface problems

The presented implementations are based on the C++ finite element library deal.II, and the methods compared include a Lagrange multiplier method, a Nitsche method derived from it, and a Nitsche method on cut elements. The primary aim is to provide a priori error estimates for each method, assessing computational cost and accuracy.

These results have been presented in a paper titled "Comparison of non-matching techniques for the finite element approximation of interface problems". The implementation leverages the capabilities of the CGAL library for computational geometry tasks, ensuring robust intersection routines. The research validates the implementations with varied experiments, considering different mesh configurations, algorithms, and boundary conditions.