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On the Properties of Operators of the Stokes Problem with Corner Singularity in Nonsymmetric Variational Formulation

Author

Listed:
  • Viktor A. Rukavishnikov

    (Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen Str. 65, 680000 Khabarovsk, Russia
    These authors contributed equally to this work.)

  • Alexey V. Rukavishnikov

    (Institute of Applied Mathematics of the Far Eastern Branch of the Russian Academy of Sciences, Dzerzhinsky Str. 54, 680000 Khabarovsk, Russia
    These authors contributed equally to this work.)

Abstract

The weighted finite element method makes it possible to find an approximate solution of a boundary value problem with corner singularity without loss of accuracy. The construction of this numerical method is based on the introduction of the concept of an R ν -generalized solution for a boundary value problem with a singularity. In this paper, special weighted sets based on the corresponding operators from the definition of the R ν -generalized solution of the Stokes problem in a nonsymmetric variational formulation are introduced. The properties and relationships of these weighted sets are established.

Suggested Citation

  • Viktor A. Rukavishnikov & Alexey V. Rukavishnikov, 2022. "On the Properties of Operators of the Stokes Problem with Corner Singularity in Nonsymmetric Variational Formulation," Mathematics, MDPI, vol. 10(6), pages 1-32, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:889-:d:768456
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    References listed on IDEAS

    as
    1. Nejmeddine Chorfi, 2014. "Geometric Singularities of the Stokes Problem," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, January.
    2. Viktor A. Rukavishnikov & Elena I. Rukavishnikova, 2020. "On the Dirichlet Problem with Corner Singularity," Mathematics, MDPI, vol. 8(11), pages 1-7, October.
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