An Improved Robin-Robin Coupling Method for Parabolic-Parabolic Interface Problems

2025/09/09 by Burman, Erik, Fernandez, Miguel A., Guzman, Johnny +1
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2509.08103

Abstract

We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [Numer. Algorithms, 99:921-948, 2025] for a parabolic-parabolic interface problem. We modify the first step of the scheme so that several error difference quantities remain higher order convergence without requiring additional assumptions. Numerical results are presented to support our findings.

Citations

• A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems
• Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method
• Loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling: unified analysis for parabolic/parabolic and parabolic/hyperbolic problems

Related

• A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems
• Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method
• Loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling: unified analysis for parabolic/parabolic and parabolic/hyperbolic problems
• An abstract approach to the Robin-Robin method
• On the stability of a loosely-coupled scheme based on a Robin interface condition for fluid-structure interaction