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arXiv · 2404.01599

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

Erik Burman·Rebecca Durst·Miguel A. Fernández·Johnny Guzmán·Sijing Liu
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Abstract

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 $\mathcal O((\Delta t)^2)$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $\Delta t$ stands for the time-step length. Numerical results are shown to support our analysis and the assumptions.

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Erik Burman, Rebecca Durst, Miguel A. Fernández, Johnny Guzmán, Sijing Liu. 2024-04-02. A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems. https://arxiv.org/abs/2404.01599

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