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Martin Campos Pinto; Eric Sonnendrücker Compatible Maxwell solvers with particles II: conforming and nonconforming 2D schemes with a strong Faraday law SMAIJournal of computational mathematics, 3 (2017), p. 91116, doi: 10.5802/smaijcm.21 Article PDF Class. Math.: 35Q61, 65M12, 65M60, 65M75 Keywords: Maxwell equations, Gauss laws, structurepreserving, PIC, chargeconserving current deposition, conforming finite elements, discontinuous Galerkin, Conga method. Abstract This article is the second of a series where we develop and analyze structurepreserving finite element discretizations for the timedependent 2D Maxwell system with longtime stability properties, and propose a chargeconserving 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 nonconforming schemes in the 3D case. Here the theory is extended to account for approximate sources, and specific chargeconserving 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 longtime stability is ensured by the natural $L^2$ projection for the current, also standard. The second one is a new nonconforming 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 nonstandard current approximation operator must be used to yield a chargeconserving scheme with longtime stability properties, while retaining the local nature of $L^2$ projections in discontinuous spaces. Numerical experiments involving Maxwell and MaxwellVlasov problems are then provided to validate the stability of the proposed methods. Bibliography [2] D.N. Arnold, R.S. Falk & R. Winther, “Geometric decompositions and local bases for spaces of finite element differential forms”, Computer Methods in Applied Mechanics and Engineering 198 (2009) no. 21, p. 16601672 Article [3] D.N. Arnold, R.S. Falk & R. Winther, “Finite element exterior calculus: from Hodge theory to numerical stability”, Bull. Amer. Math. Soc.(NS) 47 (2010) no. 2, p. 281354 Article [4] D. Boffi, F. Brezzi & M. 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