Maximum error estimates of a MAC scheme for Stokes equations with Dirichlet boundary conditions

Dong, Haixia; Ying, Wenjun; Zhang, Jiwei

doi:10.1016/j.apnum.2019.09.017

Cited by 6 publications

(1 citation statement)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, they just only obtained one and a half order accuracy about the terms near the boundary in the discrete

{H}&#x0005E;1

norms on uniform girds. Until 2020, Dong et al 19 first proved that the second‐order convergence rate in

{L}&#x0005E;2

norm for the pressure and the second‐order accuracy in

{L}&#x0005E;2

norm and maximum norm for both velocity and its gradient.…”

Section: Introductionmentioning

confidence: 99%

Modified marker and cell schemes for Stokes equations with Dirichlet boundary condition

Guo

Rui

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we proposed a modified marker and cell (MMAC) method for solving the steady‐state Stokes equations with Dirichlet boundary condition. We reconstruct the marker and cell (MAC) schemes by using the quadratic Lagrange extrapolation method to approximate the value of ghost points near the boundary. First, we prove the stability of the proposed scheme rigorously. Then, we obtain the second‐order superconvergence for pressure in the discrete L2$$ {L}^2 $$ norm and velocity in the discrete H1$$ {H}^1 $$ norm by constructing auxiliary functions and discretizing parameters. Meanwhile, we present two MMAC schemes for the time‐dependent Stokes equations by a similar method. Finally, we provide some numerical experiments to confirm our theoretical analysis.

show abstract

“…However, they just only obtained one and a half order accuracy about the terms near the boundary in the discrete