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A hybridizable discontinuous Galerkin method for the time-harmonic Maxwell equations with high wave number. (English) Zbl 1342.65216

Summary: This paper proposes and analyzes a hybridizable discontinuous Galerkin (HDG) method for the three-dimensional time-harmonic Maxwell equations coupled with the impedance boundary condition in the case of high wave number. It is proved that the HDG method is absolutely stable for all wave numbers \({\kappa>0}\) in the sense that no mesh constraint is required for the stability. A wave-number-explicit stability constant is also obtained. This is done by choosing a specific penalty parameter and using a PDE duality argument. Utilizing the stability estimate and a non-standard technique, the error estimates in both the energy-norm and the \({\mathbf{L}^{2}}\)-norm are obtained for the HDG method. Numerical experiments are provided to validate the theoretical results and to gauge the performance of the proposed HDG method.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
78A40 Waves and radiation in optics and electromagnetic theory

Software:

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References:

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