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   https://doi.org/10.1007/s10444-024-10130-x  

   Demkowicz, Leszek; Melenk, Jens M; Badger, Jacob; Henneking, Stefan (April 2024, Advances in Computational Mathematics)

   This paper is a continuation of Melenk et al., "Stability analysis for electromagnetic waveguides. Part 1: acoustic and homogeneous electromagnetic waveguides" (2023), extending the stability results for homogeneous electromagnetic (EM) waveguides to the non-homogeneous case. The analysis is done using perturbation techniques for self-adjoint operators eigenproblems. We show that the non-homogeneous EM waveguide problem is well-posed with the stability constant scaling linearly with waveguide length L. The results provide a basis for proving convergence of a Discontinuous Petrov-Galerkin (DPG) discretization based on a full envelope ansatz, and the ultraweak variational formulation for the resulting modified system of Maxwell equations, see Part 1. 

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2. Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides

   https://doi.org/10.1137/23M1599239  

   Melenk, Jens M; Demkowicz, Leszek; Henneking, Stefan (June 2025, SIAM Journal on Mathematical Analysis)

   In a time-harmonic setting, we show for heterogeneous acoustic and homogeneous electromagnetic wavesguides stability estimates with the stability constant depending linearly on the length L of the waveguide. These stability estimates are used for the analysis of the (ideal) ultraweak (UW) variant of the discontinuous Petrov--Galerkin (DPG) method. For this UW DPG, we show that the stability deterioration with L can be countered by suitably scaling the test norm of the method. We present the "full envelope approximation," a UW DPG method based on nonpolynomial ansatz functions that allows for treating long waveguides. 

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   Miniaci, M.; Pal, R. K. (October 2021, Journal of Applied Physics)
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