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A second order time-stepping scheme for parabolic interface problems with moving interfaces

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2017

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Richter, Thomas

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https://doi.org/10.1051/m2an/2016072
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ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. 2017, 51(4), pp. 1539-1560. ISSN 0764-583X. eISSN 1290-3841. Available under: doi: 10.1051/m2an/2016072

Zusammenfassung

We present a second order time-stepping scheme for parabolic problems on moving domains and interfaces. The diffusion coefficient is discontinuous and jumps across an interior interface. This causes the solution to have discontinuous derivatives in space and time. Without special treatment of the interface, both spatial and temporal discretization will be sub-optimal. For such problems, we develop a time-stepping method, based on a cG(1) Eulerian space-time Galerkin approach. We show −both analytically and numerically− second order convergence in time. Key to gaining the optimal order of convergence is the use of space-time test- and trial-functions, that are aligned with the moving interface. Possible applications are multiphase flow or fluid-structure interaction problems.

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Fachgebiet (DDC)
510 Mathematik

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Space-time finite elements, time stepping, moving interfaces, a priori error analysis

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ISO 690FREI, Stefan, Thomas RICHTER, 2017. A second order time-stepping scheme for parabolic interface problems with moving interfaces. In: ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. 2017, 51(4), pp. 1539-1560. ISSN 0764-583X. eISSN 1290-3841. Available under: doi: 10.1051/m2an/2016072
BibTex
@article{Frei2017secon-55817,
  year={2017},
  doi={10.1051/m2an/2016072},
  title={A second order time-stepping scheme for parabolic interface problems with moving interfaces},
  number={4},
  volume={51},
  issn={0764-583X},
  journal={ESAIM: Mathematical Modelling and Numerical Analysis},
  pages={1539--1560},
  author={Frei, Stefan and Richter, Thomas}
}
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