Formulation and Analysis of a Parameter-Free Stabilized Finite Element Method

@article{Bochev2015FormulationAA,
  title={Formulation and Analysis of a Parameter-Free Stabilized Finite Element Method},
  author={Pavel B. Bochev and Mauro Perego and Kara Peterson},
  journal={SIAM J. Numerical Analysis},
  year={2015},
  volume={53},
  pages={2363-2388}
}
We present a stabilized finite element method for the scalar advection-diffusion equation, which does not require tunable mesh-dependent parameters. Stabilization is achieved by using diffusive fluxes extracted from an edge element lifting of Scharfetter-Gummel edge fluxes into the elements. Although the method is formally first-order accurate, qualitative numerical studies suggest that it occupies a middle ground between an artificial diffusion and a streamline-upwind Petrov-Galerkin… CONTINUE READING

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