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Creators/Authors contains: "Melenk, Jens M"

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  1. ; ; (, 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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    Free, publicly-accessible full text available June 30, 2026
  2. ; ; ; (, 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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