Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater--Surface Water Flows

Abstract

The most effective simulations of the multiphysics coupling of groundwater to surface water must involve employing the best groundwater codes and the best surface water codes. Partitioned methods, which solve the coupled problem by successively solving the subphysics problems, have recently been studied for the Stokes--Darcy coupling with convergence established over bounded time intervals (with constants growing exponentially in $t$). This report analyzes and tests two such partitioned (noniterative, domain decomposition) methods for the fully evolutionary Stokes--Darcy problem. Under a modest time step restriction of the form $\Delta t\leq C$, where $C=C$ (physical parameters), we prove unconditional, long time (over $0\leq t<\infty $) stability of both partitioned methods. From this we derive an optimal error estimate that is uniform in time over $0\leq t<\infty$.