W\(^{1,q }\) stability of the Fortin operator for the MAC scheme

DOI10.1007/s10092-011-0045-xzbMath1248.76109OpenAlexW2015975209MaRDI QIDQ714663

Raphaèle Herbin, Thierry Gallouet, Jean-Claude Latché

Publication date: 11 October 2012

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-011-0045-x

zbMATH Keywords

MAC schemeFortin operatorprojection stability

Mathematics Subject Classification ID

Finite volume methods applied to problems in fluid mechanics (76M12) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (14)

Superconvergence analysis of the MAC scheme for the two dimensional stokes problem ⋮ A MAC scheme for coupled Stokes-Darcy equations on non-uniform grids ⋮ Stability and Superconvergence of MAC Scheme for Stokes Equations on Nonuniform Grids ⋮ An asymptotic preserving and energy stable scheme for the barotropic Euler system in the incompressible limit ⋮ Second order convergence of a modified MAC scheme for Stokes interface problems ⋮ An FFT-based MAC scheme for Stokes equations with periodic boundary conditions and its application to elasticity problems ⋮ Convergence of the fully discrete incremental projection scheme for incompressible flows ⋮ Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations ⋮ Error estimates for the implicit MAC scheme for the compressible Navier-Stokes equations ⋮ MAC finite difference scheme for Stokes equations with damping on non-uniform grids ⋮ Convergence of the marker-and-cell scheme for the semi-stationary compressible Stokes problem ⋮ Superconvergence of Characteristics Marker and Cell Scheme for the Navier--Stokes Equations on Nonuniform Grids ⋮ Stability and convergence of characteristic MAC scheme and post-processing for the Oseen equations on non-uniform grids ⋮ Maximum error estimates of a MAC scheme for Stokes equations with Dirichlet boundary conditions

Cites Work

• On the stability of colocated clustered finite volume simplicial discretizations for the 2D Stokes problem
• A quasi-local interpolation operator preserving the discrete divergence
• Convergence of the MAC Scheme for the Compressible Stokes Equations
• Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
• A Fortin operator for two-dimensional Taylor-Hood elements
• Mixed and Hybrid Finite Element Methods
• Analysis and Convergence of the MAC Scheme. I. The Linear Problem
• Analysis and convergence of the MAC scheme. II. Navier-Stokes equations
• Unnamed Item

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