An Absolutely Stable Pressure-Poisson Stabilized Finite Element Method for the Stokes Equations

@article{Bochev2004AnAS,
  title={An Absolutely Stable Pressure-Poisson Stabilized Finite Element Method for the Stokes Equations},
  author={Pavel B. Bochev and Max Gunzburger},
  journal={SIAM J. Numerical Analysis},
  year={2004},
  volume={42},
  pages={1189-1207}
}
The pressure-Poisson stabilized Galerkin method for the Stokes equation requires the choice of a positive parameter. Existing theoretical predictions for the range of parameter values that yield stable discretizations seem to be very pessimistic when compared to the computational evidence. Motivated by this wide gap, we first examine a continuous prototype for this class of schemes. We show that the prototype is absolutely stable, i.e., it is stable for all parameter values, and is optimally… CONTINUE READING
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