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An Adaptive SDG Method for the Stokes System

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Abstract

Staggered grid techniques are attractive ideas for flow problems due to their more enhanced conservation properties. Recently, a staggered discontinuous Galerkin method is developed for the Stokes system. This method has several distinctive advantages, namely high order optimal convergence as well as local and global conservation properties. In addition, a local postprocessing technique is developed, and the postprocessed velocity is superconvergent and pointwisely divergence-free. Thus, the staggered discontinuous Galerkin method provides a convincing alternative to existing schemes. For problems with corner singularities and flows in porous media, adaptive mesh refinement is crucial in order to reduce the computational cost. In this paper, we will derive a computable error indicator for the staggered discontinuous Galerkin method and prove that this indicator is both efficient and reliable. Moreover, we will present some numerical results with corner singularities and flows in porous media to show that the proposed error indicator gives a good performance.

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, SAR, People’s Republic of China

    Eric T. Chung, Jie Du & Man Chun Yuen

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  1. Eric T. Chung
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  2. Jie Du
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  3. Man Chun Yuen
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Correspondence to Jie Du.

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Chung, E.T., Du, J. & Yuen, M.C. An Adaptive SDG Method for the Stokes System. J Sci Comput 70, 766–792 (2017). https://doi.org/10.1007/s10915-016-0265-y

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  • DOI: https://doi.org/10.1007/s10915-016-0265-y

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