Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method

Burman, Erik; Durst, Rebecca; Fernández, Miguel A.; Guzmán, Johnny; Liu, Sijing

doi:10.1007/s11075-024-01902-z

Numer Algor

2024

DOI: 10.1007/s11075-024-01902-z

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Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method

Erik Burman,

Rebecca Durst,

Miguel A. Fernández

et al.

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A second-order correction method for loosely coupled discretizations applied to parabolic–parabolic interface problems

Burman,

Durst,

Fernández

et al. 2024

IMA Journal of Numerical Analysis

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We consider a parabolic–parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin–Robin splitting method analyzed in [J. Numer. Math., 31(1):59–77, 2023]. We show that the errors of the correction step converge at $\mathcal O((\varDelta t)^{2})$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $\varDelta t$ stands for the time-step length. Numerical results are shown to support our analysis and the assumptions.

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A second-order correction method for loosely coupled discretizations applied to parabolic–parabolic interface problems

Burman,

Durst,

Fernández

et al. 2024

IMA Journal of Numerical Analysis

View full text Add to dashboard Cite

show abstract

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Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method

Cited by 1 publication

References 26 publications

A second-order correction method for loosely coupled discretizations applied to parabolic–parabolic interface problems

A second-order correction method for loosely coupled discretizations applied to parabolic–parabolic interface problems

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