Understanding the Limits of Inf-Sup Stable Galerkin-FEM for Incompressible Flows
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- Lube G., Arndt D., Dallmann H. (2015) Understanding the Limits of Inf-Sup Stable Galerkin-FEM for Incompressible Flows. In: Knobloch P. (eds) Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014. Lecture Notes in Computational Science and Engineering, vol 108. Springer, Cham
The core of numerical simulations of coupled incompressible flow problems consists of a robust, accurate and fast solver for the time-dependent, incompressible Navier-Stokes equations. We consider inf-sup stable finite element methods with grad-div stabilization and symmetric stabilization of local projection type. The approach is based on a proper scale separation and only the small unresolved scales are modeled. Error estimates for the spatially discretized problem with reasonable growth of the Gronwall constant for large Reynolds numbers are given together with a critical discussion of the choice of stabilization parameters. The fast solution of the fully discretized problems (using BDF(2) in time) is accomplished via unconditionally stable velocity-pressure segregation.