Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
Jens M. Melenk, Leszek Demkowicz, Stefan Henneking
Source abstract
Abstract. 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 [Formula: see text] 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 [Formula: see text] 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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