High-order continuous and discontinuous Galerkin methods for wave problems

Author (s): Giorgiani, G.; Modesto, D.; Fernández-Méndez, S. and Huerta, A.
Journal: International Journal for Numerical Methods in Fluids

Volume: 73, Issue 10
Pages: 883 – 903
Date: 2013

Abstract:
Three Galerkin methods —continuous Galerkin (CG), Compact Discontinuous Galerkin (CDG) and Hybridizable Discontinuous Galerkin (HDG)— are compared in terms of performance and computational efficiency in two-dimensional scattering problems for low and high-order polynomial approximations. The total number of degrees of freedom and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for CG and HDG, when high-order elements are adopted, both of them clearly outperforming CDG.

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Bibtex:

@article{GG-GMFH:13,
        Author = {Giorgio Giorgiani and David Modesto and Sonia Fern\'andez-M\'endez and Antonio Huerta},
        Title = {High-order continuous and discontinuous {G}alerkin methods for wave problems},
        Fjournal = {International Journal for Numerical Methods in Fluids},
        Journal = {Int. J. Numer. Methods Fluids},
        Volume = {73},
        Number = {10},
        Pages = {883--903},
        Year = {2013}
        Doi = {10.1002/fld.3828},
        }