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 , under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where stands for the time-step length. Numerical results are shown to support our analysis and the assumptions.
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}
}