Publikation: An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain
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2024
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Singh, Maneesh Kumar
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Journal of Scientific Computing. Springer. 2024, 99(3), 64. ISSN 0885-7474. eISSN 1573-7691. Verfügbar unter: doi: 10.1007/s10915-024-02530-4
Zusammenfassung
We consider a time-stepping scheme of Crank–Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step is required. Following Lehrenfeld and Olskanskii (ESAIM: M2AN 53(2):585–614, 2019), we apply an implicit extension based on so-called ghost-penalty terms. For spatial discretisation, a cut finite element method is used. We derive a complete a priori error analysis in space and time, which shows in particular second-order convergence in time under a parabolic CFL condition. Finally, we present numerical results in two and three space dimensions that confirm the analytical estimates, even for much larger time steps.
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Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Eulerian time-stepping scheme, Time-dependent domains, Heat equation, Crank–Nicolson scheme, A priori error analysis
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FREI, Stefan, Maneesh Kumar SINGH, 2024. An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain. In: Journal of Scientific Computing. Springer. 2024, 99(3), 64. ISSN 0885-7474. eISSN 1573-7691. Verfügbar unter: doi: 10.1007/s10915-024-02530-4BibTex
@article{Frei2024Impli-69972,
title={An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain},
year={2024},
doi={10.1007/s10915-024-02530-4},
number={3},
volume={99},
issn={0885-7474},
journal={Journal of Scientific Computing},
author={Frei, Stefan and Singh, Maneesh Kumar},
note={Article Number: 64}
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