# FETI-DP for the three-dimensional Virtual Element Method

## TL;DR

This paper extends the FETI-DP preconditioner analysis to 3D virtual element methods, proving polylogarithmic condition number bounds that are independent of subdomain count, mesh size, and coefficient jumps, with numerical validation.

## Contribution

It generalizes FETI-DP preconditioning results to three-dimensional VEM, establishing bounds independent of key problem parameters.

## Key findings

- Polylogarithmic condition number bounds proven for 3D VEM.
- Bounds are independent of subdomain number, mesh size, and coefficient jumps.
- Numerical experiments confirm theoretical results.

## Abstract

We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend the result of [22] to the three dimensional case. We prove polylogarithmic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. Numerical experiments validate the theory