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A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems (2404.01599v1)

Published 2 Apr 2024 in math.NA and cs.NA

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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