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

2015/09/02 by Thomas Boiveau, Boiveau, Thomas
Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1509.00542

openalex publication_date 2015/09/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

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 H¹-convergence and L²-convergence of the error in both cases. Some numerical results are provided to corroborate the theoretical study.

Citations

• A penalty free Nitsche type method for the weak imposition of boundary conditions in compressible and incompressible elasticity

Related

• Optimal preconditioners for a Nitsche stabilized fictitious domain finite element method
• Nitsche's method under a semi-regular mesh condition
• Fictitious domain method with boundary value correction using penalty-free Nitsche method
• Optimal L² error estimation for the unfitted interface finite element method based on the non-symmetric Nitsche's methods
• Geometric Transformation of Finite Element Methods: Theory and Applications