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Online Mixed Multiscale Finite Element Method with Oversampling and Its Applications

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Abstract

In this paper, we consider an online basis enrichment mixed generalized multiscale method with oversampling, for solving flow problems in highly heterogeneous porous media. This is an extension of the online mixed generalized multiscale method (Chan et al. in Numer Math Theory Methods Appl 9(4):497–527, 2016). The multiscale online basis functions are computed by solving a Neumann problem in an over-sampled domain, instead of a standard neighborhood of a coarse face. We are motivated by the restricted domain decomposition method. Extensive numerical experiments are presented to demonstrate the performance of our methods for both steady-state flow, and two-phase flow and transport problems.

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Acknowledgements

The research of Eric Chung is partially supported by RGC and CUHK. Yanfang Yang’s work is supported by the National Natural Science Foundation of China (Grant No. 11901129).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, People’s Republic of China

    Yanfang Yang

  2. Department of Mathematics, The Chinese University of Hong Kong, Sha Tin, Hong Kong SAR

    Shubin Fu & Eric T. Chung

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  1. Yanfang Yang
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  2. Shubin Fu
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  3. Eric T. Chung
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Correspondence to Shubin Fu.

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Yang, Y., Fu, S. & Chung, E.T. Online Mixed Multiscale Finite Element Method with Oversampling and Its Applications. J Sci Comput 82, 31 (2020). https://doi.org/10.1007/s10915-019-01121-y

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  • DOI: https://doi.org/10.1007/s10915-019-01121-y

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