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Analysis of the hp-Version of a First Order System Least Squares Method for the Helmholtz Equation

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Advanced Finite Element Methods with Applications (FEM 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 128))

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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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Authors and Affiliations

  1. Technische Universität Wien, Institute for Analysis and Scientific Computing, Vienna, Austria

    Maximilian Bernkopf & Jens Markus Melenk

Authors
  1. Maximilian Bernkopf
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  2. Jens Markus Melenk
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Correspondence to Maximilian Bernkopf .

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Editors and Affiliations

  1. Institut für Mathematik & Computergestützte Simulation, Universität der Bundeswehr München, Neubiberg, Germany

    Thomas Apel

  2. Institute for Computational Mathematics, Johannes Kepler University Linz, Linz, Austria

    Ulrich Langer

  3. Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

    Arnd Meyer

  4. Institut für Angewandte Mathematik, Technische Universität Graz, Graz, Austria

    Olaf Steinbach

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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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