With cedram.org version française Home Presentation Advanced Search All online articles Latest articles Search for an article Table of contents for this volume | Previous article | Next article Martin Campos Pinto; Eric SonnendrückerCompatible Maxwell solvers with particles II: conforming and non-conforming 2D schemes with a strong Faraday lawSMAI-Journal of computational mathematics, 3 (2017), p. 91-116, doi: 10.5802/smai-jcm.21 Article PDF Class. Math.: 35Q61, 65M12, 65M60, 65M75Keywords: Maxwell equations, Gauss laws, structure-preserving, PIC, charge-conserving current deposition, conforming finite elements, discontinuous Galerkin, Conga method. AbstractThis article is the second of a series where we develop and analyze structure-preserving finite element discretizations for the time-dependent 2D Maxwell system with long-time stability properties, and propose a charge-conserving deposition scheme to extend the stability properties in the case where the current source is provided by a particle method. The schemes proposed here derive from a previous study where a generalized commuting diagram was identified as an abstract compatibility criterion in the design of stable schemes for the Maxwell system alone, and applied to build a series of conforming and non-conforming schemes in the 3D case. Here the theory is extended to account for approximate sources, and specific charge-conserving schemes are provided for the 2D case. In this second article we study two schemes which include a strong discretization of the Faraday law. The first one is based on a standard conforming mixed finite element discretization and the long-time stability is ensured by the natural $L^2$ projection for the current, also standard. The second one is a new non-conforming variant where the numerical fields are sought in fully discontinuous spaces. In this 2D setting it is shown that the associated discrete curl operator coincides with that of a classical DG formulation with centered fluxes, and our analysis shows that a non-standard current approximation operator must be used to yield a charge-conserving scheme with long-time stability properties, while retaining the local nature of $L^2$ projections in discontinuous spaces. Numerical experiments involving Maxwell and Maxwell-Vlasov problems are then provided to validate the stability of the proposed methods. Bibliography[1] D.N. Arnold, R.S. Falk & R. Winther, “Finite element exterior calculus, homological techniques, and applications”, Acta Numerica (2006) Article[2] D.N. 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