Construction and analysis of a HDG solution for the total-flux formulation of the convected Helmholtz equation

Barucq, Hélène; Rouxelin, Nathan; Tordeux, Sébastien

doi:10.1090/mcom/3850

Construction and analysis of a HDG solution for the total-flux formulation of the convected Helmholtz equation
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by Hélène Barucq, Nathan Rouxelin and Sébastien Tordeux HTML | PDF

Math. Comp. 92 (2023), 2097-2131 Request permission

Abstract:

We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.

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