Multiscale stabilization for convection-dominated diffusion in heterogeneous media

Victor M Calo Tsz Shun Eric CHUNG Yalchin Efendiev Wing Tat Leung

Numerical Analysis and Scientific Computing mathscidoc:1910.43504

Computer Methods in Applied Mechanics and Engineering, 304, 359-377, 2016.6
We develop a PetrovGalerkin stabilization method for multiscale convectiondiffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion, which may not be sufficient to stabilize multiscale systems. We seek a local reduced-order model for this kind of multiscale transport problems and thus, develop a systematic approach for finding reduced-order approximations of the solution. We start from a PetrovGalerkin framework using optimal weighting functions. We introduce an auxiliary variable to a mixed formulation of the problem. The auxiliary variable stands for the optimal weighting function. The problem reduces to finding a test space (a dimensionally reduced space for this auxiliary variable), which guarantees that the error in the primal variable (representing the solution) is close to the projection error of the full
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@inproceedings{victor2016multiscale,
  title={Multiscale stabilization for convection-dominated diffusion in heterogeneous media},
  author={Victor M Calo, Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181231139544033},
  booktitle={Computer Methods in Applied Mechanics and Engineering},
  volume={304},
  pages={359-377},
  year={2016},
}
Victor M Calo, Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung. Multiscale stabilization for convection-dominated diffusion in heterogeneous media. 2016. Vol. 304. In Computer Methods in Applied Mechanics and Engineering. pp.359-377. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181231139544033.
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