# The Superconvergence Phenomenon and Proof of the MAC Scheme for the Stokes Equations on Non-uniform Rectangular Meshes

@article{Li2015TheSP, title={The Superconvergence Phenomenon and Proof of the MAC Scheme for the Stokes Equations on Non-uniform Rectangular Meshes}, author={Jichun Li and Shuyu Sun}, journal={J. Sci. Comput.}, year={2015}, volume={65}, pages={341-362} }

- Published 2015 in J. Sci. Comput.
DOI:10.1007/s10915-014-9963-5

For decades, the widely used finite difference method on staggered grids, also known as the marker and cell (MAC) method, has been one of the simplest and most effective numerical schemes for solving the Stokes equations and Navier–Stokes equations. Its superconvergence on uniform meshes has been observed by Nicolaides (SIAM J Numer Anal 29(6):1579–1591, 1992), but the rigorous proof is never given. Its behavior on non-uniform grids is not well studied, since most publications only consider… CONTINUE READING

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#### References

##### Publications referenced by this paper.

Showing 1-10 of 26 references

## Divergence-free discontinuous Galerkin schemes for the Stokes equations and the MAC scheme ∗

View 6 Excerpts

Highly Influenced

## Finite-element error estimates for the MAC scheme

View 4 Excerpts

Highly Influenced

## Difference analogues of orthogonal decompositions, fundamental differential operators and certain boundary-value problems of mathematical physics

View 3 Excerpts

Highly Influenced

## Supercloseness of the divergence-free finite element solutions on rectangular grids

## Remarks on the links between low-order DG methods and some finite-difference schemes for the Stokes problem

View 2 Excerpts