Understanding the Limits of Inf-Sup Stable Galerkin-FEM for Incompressible Flows

DOI10.1007/978-3-319-25727-3_12zbMath1427.76136OpenAlexW2486241739MaRDI QIDQ5207416

Daniel Arndt, Helene Dallmann, Gert Lube

Publication date: 20 December 2019

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-25727-3_12

zbMATH Keywords

Oseen problemsubgrid modelStokes problemlocal mass conservationfluctuation operator

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stokes and related (Oseen, etc.) flows (76D07) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items

On the determination of the grad-div criterion, Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?, Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements, Robust error analysis of \(H(\mathrm{div})\)-conforming DG method for the time-dependent incompressible Navier-Stokes equations

Uses Software

• deal.ii

Cites Work

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• The \texttt{deal.II} library, version 8.4
• On the parameter choice in grad-div stabilization for the Stokes equations
• An adaptive residual local projection finite element method for the Navier-Stokes equations
• Analysis of a variational multiscale method for large-eddy simulation and its application to homogeneous isotropic turbulence
• On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime
• Local projection stabilization for incompressible flows: equal-order vs. inf-sup stable interpolation
• A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
• A finite element pressure gradient stabilization for the Stokes equations based on local projections
• Faedo-Galerkin weak solutions of the Navier-Stokes equations with Dirichlet boundary conditions are suitable
• A quasi-local interpolation operator preserving the discrete divergence
• Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
• Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations with pressure independent velocity errors
• Algorithms and data structures for massively parallel generic adaptive finite element codes
• A PROJECTION-BASED VARIATIONAL MULTISCALE METHOD FOR LARGE-EDDY SIMULATION WITH APPLICATION TO NON-ISOTHERMAL FREE CONVECTION PROBLEMS
• Local projection FEM stabilization for the time‐dependent incompressible <scp>N</scp>avier–<scp>S</scp>tokes problem
• A unified convergence analysis for local projection stabilisations applied to the Oseen problem
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• deal.II—A general-purpose object-oriented finite element library
• Local projection type stabilization applied to inf-sup stable discretizations of the Oseen problem
• Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers
• Error Analysis of Pressure-Correction Schemes for the Time-Dependent Stokes Equations with Open Boundary Conditions