Fitted and unfitted domain decomposition using penalty free Nitsche method for the Poisson problem with discontinuous material parameters

TL;DR

This paper analyzes a penalty-free Nitsche's method for stable domain decomposition of the Poisson problem with discontinuous parameters, covering both fitted and unfitted meshes, and proves convergence with supporting numerical results.

Contribution

It introduces and analyzes a penalty-free Nitsche's method for both fitted and unfitted domain decompositions, demonstrating stability and convergence.

Findings

Proves $H^1$-convergence and $L^2$-convergence for the method

Validates theoretical results with numerical experiments

Handles discontinuous material parameters effectively

Abstract

In this paper, we study the stability of the non symmetric version of the Nitsche's method without penalty for domain decomposition. The Poisson problem is considered as a model problem. The computational domain is divided into two subdomain that can have different material parameters. In the first half of the paper we are interested in nonconforming domain decomposition, each subdomain is meshed independently of each other. In the second half, we study unfitted domain decomposition, the computational domain has only one mesh and we allow the interface to cut elements of the mesh. The fictitious domain method is used to handle this specificity. We prove $H^1$-convergence and $L^2$-convergence of the error in both cases. Some numerical results are provided to corroborate the theoretical study.