Stabilized interior penalty methods for the time-harmonic Maxwell equations
نویسندگان
چکیده
We propose stabilized interior penalty discontinuous Galerkin methods for the indefinite time–harmonic Maxwell system. The methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field. We prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach.
منابع مشابه
Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell's equations
nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell’s equations Alexandre Ern, Jean-Luc Guermond To cite this version: Alexandre Ern, Jean-Luc Guermond. Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell’s equations. 2017. HAL Id: hal-01563594...
متن کاملInterior penalty method for the indefinite time-harmonic Maxwell equations
In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in highfrequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L-norm. In particular, the error in the energy norm is shown to converge with the optimal order O(hmin...
متن کاملMixed Discontinuous Galerkin Approximation of the Maxwell Operator
We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp. 22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods A...
متن کاملOptimal Penalty Parameters for Symmetric Discontinuous Galerkin Discretisations of the Time-Harmonic Maxwell Equations
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 para...
متن کاملAn Interior Penalty Method with C Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity
The present paper proposes and analyzes an interior penalty technique using C0-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the eigenvalue problem is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and to be spectrally cor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002