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

  • Shweta SrivastavaEmail author
  • Sashikumaar Ganesan
Article
  • 13 Downloads

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.

Keywords

Convection–diffusion–reaction equation Local projection stabilization Discontinuous Galerkin method in time Arbitrary Lagrangian Eulerian formulations 

Mathematics Subject Classification

65M12 65M60 35Q35 

Notes

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Instituto de Matematica Y Ciencias Afines (IMCA)Universidad Nacional de IngenieriaLimaPeru
  2. 2.Department of Computational and Data SciencesIndian Institute of ScienceBangaloreIndia

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