Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

2021/10/14 by Wietse M. Boon, Timo Koch, Boon, Wietse M. +5 · 1 citation
Engineering · #65F08 #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2110.07486

openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes-Darcy problem. Three different formulations and their discretizations in terms of conforming and non-conforming finite element methods and finite volume methods are considered. In each case, robust preconditioners are derived using a unified theoretical framework. In particular, the suggested preconditioners utilize operators in fractional Sobolev spaces. Numerical experiments demonstrate the parameter-robustness of the proposed solvers.

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