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Local projection stabilization with discontinuous Galerkin method in time applied to convection dominated problems in time-dependent domains

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Abstract

This paper presents the numerical analysis of a stabilized finite element scheme with discontinuous Galerkin (dG) discretization in time for the solution of a transient convection–diffusion–reaction equation in time-dependent domains. In particular, the local projection stabilization and the higher order dG time stepping scheme are used for convection dominated problems. Further, an arbitrary Lagrangian–Eulerian formulation is used to handle the time-dependent domain. The stability and error estimates are given for the proposed numerical scheme. The validation of the proposed local projection stabilization scheme with higher order dG time discretization is demonstrated with appropriate numerical examples.

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Authors and Affiliations

  1. Instituto de Matematica Y Ciencias Afines (IMCA), Universidad Nacional de Ingenieria, Lima, Peru

    Shweta Srivastava

  2. Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, 560012, India

    Shweta Srivastava & Sashikumaar Ganesan

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  1. Shweta Srivastava
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  2. Sashikumaar Ganesan
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Correspondence to Shweta Srivastava.

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Srivastava, S., Ganesan, S. Local projection stabilization with discontinuous Galerkin method in time applied to convection dominated problems in time-dependent domains. Bit Numer Math 60, 481–507 (2020). https://doi.org/10.1007/s10543-019-00783-2

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