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

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...

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Bibliographic Details
Published in:BIT Vol. 60; no. 2; pp. 481 - 507
Main Authors: Srivastava, Shweta, Ganesan, Sashikumaar
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.06.2020
Springer Nature B.V
Subjects:
Computational Mathematics and Numerical Analysis
Convection
Discretization
Domains
Finite element method
Galerkin method
Mathematics
Mathematics and Statistics
Numeric Computing
Numerical analysis
Projection
Reaction-diffusion equations
Stabilization
Time dependence
Local projection stabilization
Arbitrary Lagrangian Eulerian formulations
Convection–diffusion–reaction equation
35Q35
Discontinuous Galerkin method in time
65M60
65M12
ISSN:0006-3835, 1572-9125
Online Access:Get full text
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Summary: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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ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-019-00783-2