English

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

Numerical Analysis 2024-04-03 v1 Numerical Analysis

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

Keywords

Cite

@article{arxiv.2404.01599,
  title  = {A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems},
  author = {Erik Burman and Rebecca Durst and Miguel A. Fernández and Johnny Guzmán and Sijing Liu},
  journal= {arXiv preprint arXiv:2404.01599},
  year   = {2024}
}
R2 v1 2026-06-28T15:41:01.380Z