# A stable and optimally convergent LaTIn-Cut Finite Element Method for multiple unilateral contact problems

## TL;DR

This paper introduces a new unfitted finite element method combining CutFEM and LaTIn techniques, enabling stable, robust, and optimally convergent simulations of complex multiple-body contact problems with arbitrary geometries.

## Contribution

The paper presents a novel unfitted finite element approach integrating CutFEM and LaTIn methods, including a new P1-P1 discretisation scheme for complex contact simulations.

## Key findings

- The method is stable, robust, and optimally convergent with mesh refinement.
- It effectively handles multiple bodies with complex geometries in 3D.
- The approach demonstrates high performance and versatility in contact problem simulations.

## Abstract

In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of the interacting solids, which can be arbitrarily complex. The key novelty of the approach is the combination of elements of the CutFEM technology, namely the enrichment of the solution field via the definition of overlapping fictitious domains with a dedicated penalty-type regularisation of discrete operators, and the LaTIn hybrid-mixed formulation of complex interface conditions. Furthermore, the novel P1-P1 discretisation scheme that we propose for the unfitted LaTIn solver is shown to be stable, robust and optimally convergent with mesh refinement. Finally, the paper introduces a high-performance 3D level-set/CutFEM framework for the versatile and robust solution of contact problems involving multiple bodies of complex geometries, with more than two bodies interacting at a single point.