Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations

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Sarmany, D. and Izsák, F. and Vegt, J.J.W. van der (2010) Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations. Journal of Scientific Computing, 44 (3). pp. 219-254. ISSN 0885-7474

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Abstract:We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are (i) valid in the pre-asymptotic regime; (ii) solely depend on the geometry and the polynomial order; and (iii) are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order (p = 1, 2, 3, 4) hierarchic H(curl)-conforming polynomial basis functions.
Item Type:Article
Additional information:Open Access
Copyright:© 2010 The Author(s)
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/73800
Official URL:http://dx.doi.org/10.1007/s10915-010-9366-1
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