A Second-Order Correction Method for Loosely Coupled Discretizations Applied to Parabolic-Parabolic Interface Problems

We consider a parabolic-parabolic interface problem and construct a looselycoupled prediction-correction scheme based on the Robin-Robin splitting methodanalyzed in [J. Numer. Math., 31(1):59–77, 2023]. We show that the errors ofthe correction step converge at 𝒪((Δ t)^2), under suitableconvergence rate assumptions on the discrete time derivative of the predictionstep, where Δ t stands for the time-step length. Numerical results areshown to support our analysis and the assumptions.