# The INTERNODES method for the treatment of non-conforming multipatch geometries in Isogeometric Analysis

## TL;DR

This paper introduces the INTERNODES method for effectively solving elliptic problems in isogeometric analysis on non-conforming multipatch geometries, ensuring optimal convergence and robustness.

## Contribution

The paper presents a novel interpolation-based INTERNODES method that handles non-conforming interfaces in isogeometric analysis, including implementation details and robustness analysis.

## Key findings

- Achieves optimal convergence rates with respect to mesh size.
- Robust against coefficient jumps in the problem.
- Supports non-conforming NURBS geometries and spaces.

## Abstract

In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that, on each interface of the configuration, exploits two independent interpolation operators to enforce the continuity of the traces and of the normal derivatives. INTERNODES supports non-conformity on NURBS spaces as well as on geometries. We specify how to set up the interpolation matrices on non-conforming interfaces, how to enforce the continuity of the normal derivatives and we give special attention to implementation aspects. The numerical results show that INTERNODES exhibits optimal convergence rate with respect to the mesh size of the NURBS spaces an that it is robust with respect to jumping coefficients.