An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain-Reference-Cited by-同舟云学术

An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain

Published:2024-04-22 Issue:3 Volume:99 Page:
ISSN:0885-7474
Container-title:Journal of Scientific Computing
language:en
Short-container-title:J Sci Comput

Author:

Frei Stefan^ORCID,Singh Maneesh Kumar

Abstract

AbstractWe 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.

Funder

Universität Konstanz

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s10915-024-02530-4.pdf

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