Space-Time Hybridizable Discontinuous Galerkin Method for the Advection–Diffusion Equation on Moving and Deforming Meshes

Sander Rhebergen () and Bernardo Cockburn ()
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Sander Rhebergen: University of Minnesota, School of Mathematics
Bernardo Cockburn: University of Minnesota, School of Mathematics

A chapter in The Courant–Friedrichs–Lewy (CFL) Condition, 2013, pp 45-63 from Springer

Abstract: Abstract We present the first space-time hybridizable discontinuous Galerkin finite element method for the advection–diffusion equation. Space-time discontinuous Galerkin methods have been proven to be very well suited for moving and deforming meshes which automatically satisfy the so-called Geometric Conservation law, for being able to provide higher-order accurate approximations in both time and space by simply increasing the degree of the polynomials used for the space-time finite elements, and for easily handling space-time adaptivity strategies. The hybridizable discontinuous Galerkin methods we introduce here add to these advantages their distinctive feature, namely, that the only globally-coupled degrees of freedom are those of the approximate trace of the scalar unknown. This results in a significant reduction of the size of the matrices to be numerically inverted, a more efficient implementation, and even better accuracy. We introduce the method, discuss its implementation and numerically explore its convergence properties.

Keywords: Discontinuous Galerkin methods; Advection–diffusion equations; Space-time methods (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8394-8_4

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DOI: 10.1007/978-0-8176-8394-8_4

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