A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem
Journal article, 2014

We present a novel finite element method for the Stokes problem on fictitious domains. We prove inf-sup stability, optimal order convergence and uniform boundedness of the condition number of the discrete system. The finite element formulation is based on a stabilized Nitsche method with ghost penalties for the velocity and pressure to obtain stability in the presence of small cut elements. We demonstrate for the first time the applicability of the Nitsche fictitious domain method to three-dimensional Stokes problems. We further discuss a general, flexible and freely available implementation of the method and present numerical examples supporting the theoretical results.

Nitsche's method

Stabilized finite element methods

Fictitious domain

Stokes problem


A. Massing

Simula Research Laboratory

M. G. Larson

Umeå University

Anders Logg

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

M. E. Rognes

Simula Research Laboratory

Journal of Scientific Computing

0885-7474 (ISSN) 1573-7691 (eISSN)

Vol. 61 3 604-628

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