Coupling nonlinear Stokes and Darcy flow using mortar finite elements

Vincent J. Ervin, Eleanor W. Jenkins, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
Original languageEnglish (US)
Pages (from-to)1198-1222
Number of pages25
JournalApplied Numerical Mathematics
Volume61
Issue number11
DOIs
StatePublished - Nov 2011

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Numerical Analysis

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