Stability and superconvergence of MAC schemes for time dependent Stokes equations on nonuniform grids

DOI10.1016/j.jmaa.2018.06.068zbMath1426.65126OpenAlexW2811411584MaRDI QIDQ724716

Xiao-Li Li, Hong-Xing Rui

Publication date: 26 July 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.06.068

zbMATH Keywords

stabilitysuperconvergencenonuniformMAC schemestime dependent Stokes equations

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (5)

Nonexistence for nonlinear hyperbolic inequalities in an annulus ⋮ 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 ⋮ Modified marker and cell schemes for Stokes equations with Dirichlet boundary condition ⋮ Error Analysis of the SAV-MAC Scheme for the Navier--Stokes Equations

Cites Work

• The superconvergence phenomenon and proof of the MAC scheme for the Stokes equations on non-uniform rectangular meshes
• Quadratic convergence for cell-centered grids
• An analysis of a mixed finite element method for the Navier-Stokes equations
• Conservation properties of unstructured staggered mesh schemes
• An \(hp\)-Galerkin method with fast solution for linear peridynamic models in one dimension
• Block-centered finite difference methods for parabolic equation with time-dependent coefficient
• Remarks on the links between low-order DG methods and some finite-difference schemes for the Stokes problem
• Analysis and Convergence of the MAC Scheme. I. The Linear Problem
• A Convergence Analysis of Yee’s Scheme on Nonuniform Grids
• A New Mixed Finite Element Formulation and the MAC Method for the Stokes Equations
• Finite-element error estimates for the MAC scheme
• Stability and Superconvergence of MAC Scheme for Stokes Equations on Nonuniform Grids
• Discrete Conservation Properties of Unstructured Mesh Schemes
• Divergence‐free discontinuous Galerkin schemes for the Stokes equations and the MAC scheme
• Characteristic block-centred finite difference methods for nonlinear convection-dominated diffusion equation

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