Abstract
Extending the wavenumber-explicit analysis of Chen and Qiu (J Comput Appl Math, 309:145–162, 2017), we analyze the L 2-convergence of a least squares method for the Helmholtz equation with wavenumber k. For domains with an analytic boundary, we obtain improved rates in the mesh size h and the polynomial degree p under the scale resolution condition that hk∕p is sufficiently small and \(p/\log k\) is sufficiently large.
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Acknowledgements
MB is grateful for the financial support by the Austrian Science Fund (FWF) through the doctoral school Dissipation and dispersion in nonlinear PDEs (grant W1245). MB thanks the workgroup of Joachim Schöberl (TU Wien) for help regarding the numerical experiments.
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Bernkopf, M., Melenk, J.M. (2019). Analysis of the hp-Version of a First Order System Least Squares Method for the Helmholtz Equation. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-14244-5_4
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