Stabilized finite element methods for the generalized Oseen problem

By Malte Braack, Erik Burman, Volker John, Gert Lube. 2007

207 citations recorded by the source corpus.

The numerical solution of the non-stationary, incompressible NavierStokes model can be split into linearized auxiliary problems of Oseen type. We present in a unique way different stabilization techniques of finite element schemes on isotropic meshes. First we describe the state-of-the-art for the classical residual-based SUPG/PSPG method. Then we discuss recent symmetric stabilization techniques which avoid some drawbacks of the classical method. These methods are closely related to the concept of variational multiscale methods which seems to provide a new approach to large eddy simulation. Finally, we give a critical comparison of these methods.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fa0423d2f387f908f1f67d335af9fe5af40301a0

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime (2014, methodology): “In mixed finite elements it is traditionally tried to get around with poor mass conservation by stabilization techniques like grad-div stabilization[23, 43, 40, 39, 34, 27, 5, 10, 38] or by variable transformations reducing the complexity of the continuous pressure[26, 47].”
Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations (2015, background): “In fact, in the FE literature, stabilization coefficients may depend on the mesh size and on the magnitude of the solution [52].”
Topology optimisation for natural convection problems (2014, background): “[63], including the element Brinkman coefficient makes sure that the stabilisation takes the reaction/porositydominance into account when the inverse permeability is large (solid and intermediate regions).”
Grad–div stabilization and subgrid pressure models for the incompressible Navier–Stokes equations (2009, methodology): “In this case the pressure may be under-resolved by lower order polynomials and an additional modeling for suppressing the related instability is needed [7,20,29,40].”
A projection-based stabilized finite element method for steady-state natural convection problem (2011, unknown): “Overviews of some common stabilization mechanisms for convection diffusion equation and Oseen problem were given in [4,22].”
A UNIFIED CONVERGENCE ANALYSIS FOR LOCAL PROJECTION STABILISATIONS APPLIED TO THE OSEEN PROBLEM (2007, methodology): “In applications, the projection P H : Y h → Y 2 h in the two-level approach has been often chosen as the global Lagrange interpolant I 2 h,r into Y 2 h [4,7–9,11,32].”