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On averaged exponential integrators for semilinear wave equations with solutions of low-regularity

Author

Listed:
  • Simone Buchholz

    (Karlsruhe Institute of Technology)

  • Benjamin Dörich

    (Karlsruhe Institute of Technology)

  • Marlis Hochbruck

    (Karlsruhe Institute of Technology)

Abstract

In this paper we introduce a class of second-order exponential schemes for the time integration of semilinear wave equations. They are constructed such that the established error bounds only depend on quantities obtained from a well-posedness result of a classical solution. To compensate missing regularity of the solution the proofs become considerably more involved compared to a standard error analysis. Key tools are appropriate filter functions as well as the integration-by-parts and summation-by-parts formulas. We include numerical examples to illustrate the advantage of the proposed methods.

Suggested Citation

  • Simone Buchholz & Benjamin Dörich & Marlis Hochbruck, 2021. "On averaged exponential integrators for semilinear wave equations with solutions of low-regularity," Partial Differential Equations and Applications, Springer, vol. 2(2), pages 1-27, April.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:2:d:10.1007_s42985-020-00045-9
    DOI: 10.1007/s42985-020-00045-9
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