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Runge–Kutta approximation for $$C_0$$ C 0 -semigroups in the graph norm with applications to time domain boundary integral equations

Author

Listed:
  • Alexander Rieder

    (Universität Wien)

  • Francisco-Javier Sayas

    (University of Delaware)

  • Jens Markus Melenk

    (Technische Universität Wien)

Abstract

We consider the approximation of an abstract evolution problem with inhomogeneous side constraint using A-stable Runge–Kutta methods. We derive a priori estimates in norms other than the underlying Banach space. Most notably, we derive estimates in the graph norm of the generator. These results are used to study convolution quadrature based discretizations of a wave scattering and a heat conduction problem.

Suggested Citation

  • Alexander Rieder & Francisco-Javier Sayas & Jens Markus Melenk, 2020. "Runge–Kutta approximation for $$C_0$$ C 0 -semigroups in the graph norm with applications to time domain boundary integral equations," Partial Differential Equations and Applications, Springer, vol. 1(6), pages 1-47, December.
    • Handle: RePEc:spr:pardea:v:1:y:2020:i:6:d:10.1007_s42985-020-00051-x
    DOI: 10.1007/s42985-020-00051-x
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