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# 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} }

- Published 2012 in J. Comput. Physics
DOI:10.1016/j.jcp.2012.06.028

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