A Constraint energy minimizing generalized multiscale finite element method for parabolic equations

Mengnan Li Tsz Shun Eric CHUNG Lijian Jiang

Numerical Analysis and Scientific Computing mathscidoc:1910.43588

Multiscale Modeling & Simulation, 17, (3), 996-1018
In this paper, we present a constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media. We will present the construction of CEM-GMsFEM and rigorously analyze its convergence for the parabolic equations. The convergence rate is characterized by the coarse grid size and the eigenvalue decay of local spectral problems, but is independent of the scale length and contrast of the media. The analysis shows that the method has a first order convergence rate with respect to coarse grid size in the energy norm and second order convergence rate with respect to coarse grid size in L^2 norm under some appropriate assumptions. For the temporal discretization, finite difference techniques are used and the convergence analysis of full discrete scheme is given. Moreover, a posteriori error estimator is
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@inproceedings{mengnana,
  title={A Constraint energy minimizing generalized multiscale finite element method for parabolic equations},
  author={Mengnan Li, Tsz Shun Eric CHUNG, and Lijian Jiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020203313243207117},
  booktitle={Multiscale Modeling & Simulation},
  volume={17},
  number={3},
  pages={996-1018},
}
Mengnan Li, Tsz Shun Eric CHUNG, and Lijian Jiang. A Constraint energy minimizing generalized multiscale finite element method for parabolic equations. Vol. 17. In Multiscale Modeling & Simulation. pp.996-1018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020203313243207117.
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