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}
}
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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