Improved stability and error analysis for a class of local projection stabilizations applied to the Oseen problem

DOI10.1002/num.21706zbMath1343.76019OpenAlexW1966324865WikidataQ112879012 ScholiaQ112879012MaRDI QIDQ4903217

Knobloch, Petr, Tobiska, Lutz

Publication date: 21 January 2013

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.21706

zbMATH Keywords

finite element methodconvectioninf-sup conditionoptimal error estimation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

A new projection-based stabilized method for steady convection-dominated convection-diffusion equations ⋮ A two-level higher order local projection stabilization on hexahedral meshes ⋮ Local projection stabilized finite element methods for advection-reaction problems ⋮ A new streamline diffusion finite element method for the generalized Oseen problem ⋮ An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems ⋮ A New L² Projection Method for the Oseen Equations ⋮ A stabilized Nitsche cut finite element method for the Oseen problem ⋮ Generalized local projection stabilized nonconforming finite element methods for Darcy equations ⋮ Edge patch-wise local projection stabilized nonconforming FEM for the Oseen problem

Cites Work

• Unnamed Item
• The two-level local projection stabilization as an enriched one-level approach
• On the relationship of local projection stabilization to other stabilized methods for one-dimensional advection-diffusion equations
• Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions
• Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods
• A finite element pressure gradient stabilization for the Stokes equations based on local projections
• Theory and practice of finite elements.
• Optimal control of the convection-diffusion equation using stabilized finite element methods
• Stabilized finite element methods for the generalized Oseen problem
• On the stability of finite-element discretizations of convection-diffusion-reaction equations
• A Generalization of the Local Projection Stabilization for Convection-Diffusion-Reaction Equations
• A unified convergence analysis for local projection stabilisations applied to the Oseen problem
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Optimal Control in Fluid Mechanics by Finite Elements with Symmetric Stabilization
• Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems
• Recent Results on Local Projection Stabilization for Convection-Diffusion and Flow Problems
• On the Application of Local Projection Methods to Convection–Diffusion–Reaction Problems
• Analysis of a Streamline Diffusion Finite Element Method for the Stokes and Navier–Stokes Equations
• Local Projection Stabilization for the Oseen Problem and its Interpretation as a Variational Multiscale Method
• Applying Local Projection Stabilization to inf-sup Stable Elements