Analysis of the PSPG method for the transient Stokes problem

DOI10.1016/j.cma.2011.05.001zbMath1230.76022OpenAlexW2091693457MaRDI QIDQ660281

Erik Burman, Miguel Ángel Fernández

Publication date: 1 February 2012

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00426777/file/RR-7074.pdf

zbMATH Keywords

stabilityfinite element methodstabilizationtime-discretizationPSPGtransient Stokes

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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 (9)

Error analysis of projection methods for non inf-sup stable mixed finite elements. The transient Stokes problem ⋮ On Really Locking-Free Mixed Finite Element Methods for the Transient Incompressible Stokes Equations ⋮ Error analysis of projection methods for non inf-sup stable mixed finite elements: the Navier-Stokes equations ⋮ High-order discretization of a stable time-domain integral equation for 3D acoustic scattering ⋮ Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem ⋮ Numerical study of the use of residual- and non-residual-based stabilized VMS formulations for incompressible power-law fluids ⋮ Analysis of the Pressure Stabilized Petrov--Galerkin Method for the Evolutionary Stokes Equations Avoiding Time Step Restrictions ⋮ An efficient Chorin-Temam projection proper orthogonal decomposition based reduced-order model for nonstationary Stokes equations ⋮ Simplified subgrid multiscale stabilized finite element method in the transient framework for Stokes equations

Uses Software

• FreeFem++

Cites Work

• Finite element approximation of the Navier-Stokes equations
• Consistent SUPG-method for transient transport problems: stability and convergence
• On inf--sup stabilized finite element methods for transient problems
• Pressure stabilization of finite element approximations of time-dependent incompressible flow problems
• On a multiscale approach to the transient Stokes problem: dynamic subscales and anisotropic space-time discretization
• 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 formulation for the Stokes problem allowing equal velocity-pressure interpolation
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Stability of time-splitting schemes for the Stokes problem with stabilized finite elements
• On stabilized finite element methods for the Stokes problem in the small time step limit
• Continuous Interior Penalty Finite Element Method for Oseen's Equations
• The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
• An Absolutely Stable Pressure-Poisson Stabilized Finite Element Method for the Stokes Equations
• Analysis of a Streamline Diffusion Finite Element Method for the Stokes and Navier–Stokes Equations
• Galerkin Finite Element Methods with Symmetric Pressure Stabilization for the Transient Stokes Equations: Stability and Convergence Analysis
• Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory
• ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES

This page was built for publication: Analysis of the PSPG method for the transient Stokes problem