Analysis of the Pressure Stabilized Petrov-Galerkin Method for the Evolutionary Stokes Equations Avoiding Time Step Restrictions

@article{John2015AnalysisOT,
  title={Analysis of the Pressure Stabilized Petrov-Galerkin Method for the Evolutionary Stokes Equations Avoiding Time Step Restrictions},
  author={Volker John and Julia Novo},
  journal={SIAM J. Numerical Analysis},
  year={2015},
  volume={53},
  pages={1005-1031}
}
Optimal error estimates for the pressure stabilized Petrov–Galerkin method for the evolutionary Stokes equations are proved, in the case of regular solutions, without restriction on the length of the time step. These results clarify the “instability of the discrete pressure for small time steps” reported in the literature. First, the limit situation of the continuous-in-time discretization is considered and second the numerical analysis for the backward Euler scheme is carried out. The main… CONTINUE READING

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