A stabilized Nitsche cut finite element method for the Oseen problem

We provide the numerical analysis for a Nitsche-based cut finite element formulation for the Oseen problem, which has been originally presented for the incompressible Navier–Stokes equations by Schott and Wall (2014) and allows the boundary of the domain to cut through the elements of an easy-to-gen...

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Bibliographic Details
Published in:	Computer methods in applied mechanics and engineering Vol. 328; pp. 262 - 300
Main Authors:	Massing, A., Schott, B., Wall, W.A.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.01.2018 Elsevier BV
Subjects:	Boundary conditions Computational fluid dynamics Continuous interior penalty stabilization Cut finite elements Dirichlet problem Fictitious domain method Finite element analysis Finite element method Fluid flow Mathematical analysis Mesh generation Navier-Stokes equations Nitsche's method Numerical analysis Oseen problem Pressure gradients Stokes law (fluid mechanics) Navier–Stokes equations Oseen problem Fictitious domain method Cut finite elements Nitsche’s method Continuous interior penalty stabilization
ISSN:	0045-7825, 1879-2138, 1879-2138
Online Access:	Get full text
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Summary:	We provide the numerical analysis for a Nitsche-based cut finite element formulation for the Oseen problem, which has been originally presented for the incompressible Navier–Stokes equations by Schott and Wall (2014) and allows the boundary of the domain to cut through the elements of an easy-to-generate background mesh. The formulation is based on the continuous interior penalty (CIP) method of Burman et al. (2006) which penalizes jumps of velocity and pressure gradients over inter-element faces to counteract instabilities arising for high local Reynolds numbers and the use of equal order interpolation spaces for the velocity and pressure. Since the mesh does not fit the boundary, Dirichlet boundary conditions are imposed weakly by a stabilized Nitsche-type approach. The addition of CIP-like ghost-penalties in the boundary zone allows to prove that our method is inf–supstable and to derive optimal order a priori error estimates in an energy-type norm, irrespective of how the boundary cuts the underlying mesh. All applied stabilization techniques are developed with particular emphasis on low and high Reynolds numbers. Two- and three-dimensional numerical examples corroborate the theoretical findings. Finally, the proposed method is applied to solve the transient incompressible Navier–Stokes equations on a complex geometry. [Display omitted] •A stabilized cut finite element method for the Oseen problem is analyzed.•Continuous interior penalty stabilizations in the interior of the domain are used.•Ghost penalties guarantee optimality and stability independent of mesh intersection.•A stabilized Nitsche-type method is utilized to impose boundary conditions weakly.•Stability and optimal order a priori error estimates are derived.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0045-7825 1879-2138 1879-2138
DOI:	10.1016/j.cma.2017.09.003