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- W4293833915 abstract "One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell’s equations is to render their hyperbolic character to elliptic form. This paper is devoted to the study of a stabilized linear, domain decomposition, finite element method for the time harmonic Maxwell’s equations, in a dual form, obtained through the Laplace transformation in time. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. The discrete problem is coercive in a symmetrized norm, equivalent to the discrete norm of the model problem. This yields discrete stability, which together with continuity guarantees the well-posedness of the discrete problem, cf Arnold et al. (2002) [3], Di Pietro and Ern (2012) [45]. The convergence is addressed both in a priori and a posteriori settings. In the a priori error estimates we confirm the theoretical convergence of the scheme in a L2-based, gradient dependent, triple norm. The order of convergence is O(h) in weighted Sobolev space Hw2(Ω), and hence optimal. Here, the weight w≔w(ɛ,s) where ɛ is the dielectric permittivity function and s is the Laplace transformation variable. We also derive, similar, optimal a posteriori error estimates controlled by a certain, weighted, norm of the residuals of the computed solution over the domain and at the boundary (involving the relevant jump terns) and hence independent of the unknown exact solution. The a posteriori approach is used, e.g. in constructing adaptive algorithms for the computational purposes, which is the subject of a forthcoming paper. Finally, through implementing several numerical examples, we validate the robustness of the proposed scheme." @default.
- W4293833915 created "2022-08-31" @default.
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- W4293833915 date "2023-02-01" @default.
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- W4293833915 title "A stabilized <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e399 altimg=si8.svg><mml:mrow><mml:mi>P</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:math> domain decomposition finite element method for time harmonic Maxwell’s equations" @default.
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- W4293833915 doi "https://doi.org/10.1016/j.matcom.2022.08.013" @default.
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