Variational multiscale stabilization of high-order spectral elements for the advection-diffusion equation

@article{Marras2012VariationalMS,
  title={Variational multiscale stabilization of high-order spectral elements for the advection-diffusion equation},
  author={Simone Marras and James F. Kelly and Frank X. Giraldo and Mariano V{\'a}zquez},
  journal={J. Comput. Physics},
  year={2012},
  volume={231},
  pages={7187-7213}
}
One major issue in the accurate solution of convection-dominated problems by means of high-order methods is the ability of the solver to maintain monotonicity. This problem is critical for spectral elements, where Gibbs oscillations may pollute the solution. However, typical filter-based stabilization techniques used with spectral elements are not monotone. In this paper, residual-based stabilization methods originally derived for finite elements are constructed and applied to high-order… CONTINUE READING

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