Assessment of Nitsche's method for Dirichlet boundary conditions treatment

Reda Mekhlouf, Abdelkader Baggag, Lakhdar Remaki

Research output: Contribution to journalConference article

Abstract

One of the big advantages of the standard finite element method is its efficiency in treating complicated geometries and imposing the associated boundary conditions. However in some cases, such as handling the Dirichlet-type boundary conditions, the stability and the accuracy of FEM are seriously compromised. In this work, Nitsche's method is introduced, as an efficient way of expressing the Dirichlet boundary conditions in the weak formulation. It is shown that Nitsche's method preserves the rate of convergence and gives more accuracy than the classical approach. The method is implemented for the simplest case of Poisson equation, for Stokes flow and Navier-Stokes equations, with slip and no-slip boundary conditions, in the case of viscous Newtonian incompressible flows. Error norms are calculated on different meshes in terms of size, topology and adaptivity, for a fair assessment of the proposed Nitsche's method.

Original languageEnglish
JournalInternational Conference on Fluid Flow, Heat and Mass Transfer
Publication statusPublished - 1 Jan 2016
Event3rd International Conference on Fluid Flow, Heat and Mass Transfer, FFHMT 2016 - Ottawa, Canada
Duration: 2 May 20163 May 2016

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Boundary conditions
Finite element method
Incompressible flow
Poisson equation
Convergence of numerical methods
Navier Stokes equations
Topology
Geometry

Keywords

  • Boundary methods
  • FEM
  • Navier-Stokes with slip and no-slip boundary conditions
  • Nitsche's method

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

Cite this

Assessment of Nitsche's method for Dirichlet boundary conditions treatment. / Mekhlouf, Reda; Baggag, Abdelkader; Remaki, Lakhdar.

In: International Conference on Fluid Flow, Heat and Mass Transfer, 01.01.2016.

Research output: Contribution to journalConference article

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