Convergence Analysis of a Discontinuous Galerkin Method with Plane Waves and Lagrange Multipliers for the Solution of Helmholtz Problems

@article{Amara2009ConvergenceAO,
  title={Convergence Analysis of a Discontinuous Galerkin Method with Plane Waves and Lagrange Multipliers for the Solution of Helmholtz Problems},
  author={Mohamed Amara and Rabia Djellouli and Charbel Farhat},
  journal={SIAM J. Numer. Anal.},
  year={2009},
  volume={47},
  pages={1038-1066}
}
We analyze the convergence of a discontinuous Galerkin method (DGM) with plane waves and Lagrange multipliers that was recently proposed by Farhat, Harari, and Hetmaniuk [Comput. Methods Appl. Mech. Engrg., 192 (2003), pp. 1389-1419] for solving two-dimensional Helmholtz problems at relatively high wavenumbers. We prove that the underlying hybrid variational formulation is well-posed. We also present various a priori error estimates that establish the convergence and order of accuracy of the… 

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