Abstract
We show that a version of the Discontinuous Galerkin Method (DGM) can be included in the Gradient Discretisation Method (GDM) framework. We prove that it meets the main mathematical gradient discretisation properties on any kind of polytopal mesh, and that it is identical to the Symmetric Interior Penalty Galerkin (SIPG) method in the case of first order polynomials. A numerical study shows the effect of the numerical parameter included in the scheme.
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References
Di Pietro, D.A., Ern, A.: Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations. Math. Comp. 79(271), 1303–1330 (2010). doi:10.1090/S0025-5718-10-02333-1
Di Pietro, D.A., Ern, A.: Mathematical aspects of discontinuous Galerkin methods. Mathématiques & Applications (Mathematics & Applications), vol. 69. Springer, Berlin (2012). doi:10.1007/978-3-642-22980-0
Droniou, J., Eymard, R., Gallouët, T., Guichard, C., Herbin, R.: The gradient discretisation method (2016). Working paper or preprint. https://hal.archives-ouvertes.fr/hal-01382358
Epshteyn, Y., Rivière, B.: Estimation of penalty parameters for symmetric interior penalty Galerkin methods. J. Comput. Appl. Math. 206(2), 843–872 (2007)
Eymard, R., Guichard, C., Herbin, R.: Small-stencil 3d schemes for diffusive flows in porous media. M2AN 46, 265–290 (2012)
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Eymard, R., Guichard, C. (2017). DGM, an Item of GDM. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_25
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DOI: https://doi.org/10.1007/978-3-319-57397-7_25
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