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 language | English |
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Journal | International Conference on Fluid Flow, Heat and Mass Transfer |
Volume | 0 |
DOIs | |
Publication status | Published - 2016 |
Event | 3rd International Conference on Fluid Flow, Heat and Mass Transfer, FFHMT 2016 - Ottawa, Canada Duration: 2 May 2016 → 3 May 2016 |
Keywords
- Boundary methods
- FEM
- Navier-Stokes with slip and no-slip boundary conditions
- Nitsche's method