Work

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

Year: 2024

Type: article

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 $\mathcal O((\varDelta t)^{2})$, 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.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/drae075

Authors: Erik Burman, Rebecca Durst, Miguel A Fernández, Johnny Guzmán, Sijing Liu