Robin–Robin domain decomposition methods for the steady-state Stokes–Darcy system with the Beavers–Joseph interface condition

Authors:
Yanzhao Cao;Max Gunzburger;Xiaoming He;Xiaoming Wang
Affiliations:
Auburn University, Department of Mathematics and Statistics, 36830, Auburn, AL, USA;Florida State University, Department of Scientific Computing, 32306-4120, Tallahassee, FL, USA;Florida State University, Department of Scientific Computing, 32306-4120, Tallahassee, FL, USA and Missouri University of Science and Technology, Department of Mathematics and Statistics, 65409, R ...;Florida State University, Department of Mathematics, 32306, Tallahassee, FL, USA
Venue:
Numerische Mathematik
Year:
2011

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Abstract

Domain decomposition methods for solving the coupled Stokes–Darcy system with the Beavers–Joseph interface condition are proposed and analyzed. Robin boundary conditions are used to decouple the Stokes and Darcy parts of the system. Then, parallel and serial domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence of the two methods is demonstrated and the results of computational experiments are presented to illustrate the convergence.