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Pressure Recovery for Weakly Over-Penalized Discontinuous Galerkin Methods for the Stokes Problem

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Abstract

In this paper, two postprocessing procedures for pressure recovery are proposed and analyzed for the weakly over-penalized discontinuous Galerkin methods developed in Liu in SIAM J Numer Anal 49:2165–2181, 2011 for the Stokes problem in two dimensions. These pressure recovery procedures are just elementwise calculations, benefiting from the weak over-penalization in the corresponding velocity schemes. There is no need for solving any discrete linear system in pressure recovery. It is proved that these recovery procedures have optimal order of convergence rates in the \( L^2 \)-norm for the numerical pressure. Three benchmark examples are tested to illustrate the accuracy and efficiency of these procedures.

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Authors and Affiliations

  1. Department of Mathematics, Yantai University, Yantai, Shandong, China

    Min Yang

  2. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523-1874, USA

    Jiangguo Liu

  3. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong

    Yanping Lin

Authors
  1. Min Yang
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  2. Jiangguo Liu
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  3. Yanping Lin
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Corresponding author

Correspondence to Jiangguo Liu.

Additional information

M. Yang was partially supported by Shandong Province Natural Science Foundation (ZR2010AQ020) and National Natural Science Foundation of China (No. 11201405). J. Liu was partially supported by the US National Science Foundation under Grant DMS-0915253. Y. Lin was partially supported by GRF grant of Hong Kong (PolyU B-Q30J ) and PolyU 8-ZDA2 and JRI of PolyU.

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Yang, M., Liu, J. & Lin, Y. Pressure Recovery for Weakly Over-Penalized Discontinuous Galerkin Methods for the Stokes Problem. J Sci Comput 63, 699–715 (2015). https://doi.org/10.1007/s10915-014-9911-4

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  • DOI: https://doi.org/10.1007/s10915-014-9911-4

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