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Development of Pressure-Robust Discontinuous Galerkin Finite Element Methods for the Stokes Problem

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Abstract

Pressure-robustness is an essential demand for the incompressible fluid simulation. In this paper, we develop the enhanced discontinuous Galerkin (DG) finite element methods for solving Stokes equations in the primary velocity-pressure formulation to achieve pressure-robustness. The velocity reconstruction operator has been designed for discontinuous functions and utilized to modify the external source assembling. The new schemes stay almost the same as that in the existing DG schemes but only differ for the source terms. The conforming discontinuous Galerkin and symmetric interior penalty DG have been employed to demonstrate the enhancement. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Several numerical experiments are performed to validate our theoretical conclusions.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30605, USA

    Lin Mu

  2. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Xiu Ye

  3. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Shangyou Zhang

Authors
  1. Lin Mu
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  2. Xiu Ye
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  3. Shangyou Zhang
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Correspondence to Lin Mu.

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The research of the second author was supported in part by National Science Foundation Grant DMS-1620016.

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Mu, L., Ye, X. & Zhang, S. Development of Pressure-Robust Discontinuous Galerkin Finite Element Methods for the Stokes Problem. J Sci Comput 89, 26 (2021). https://doi.org/10.1007/s10915-021-01634-5

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  • DOI: https://doi.org/10.1007/s10915-021-01634-5

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