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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems
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by Yanzhao Cao, Max Gunzburger, Xiaoming He and Xiaoming Wang PDF
Math. Comp. 83 (2014), 1617-1644 Request permission


Two parallel, non-iterative, multi-physics, domain decomposition methods are proposed to solve a coupled time-dependent Stokes-Darcy system with the Beavers-Joseph-Saffman-Jones interface condition. For both methods, spatial discretization is effected using finite element methods. The backward Euler method and a three-step backward differentiation method are used for the temporal discretization. Results obtained at previous time steps are used to approximate the coupling information on the interface between the Darcy and Stokes subdomains at the current time step. Hence, at each time step, only a single Stokes and a single Darcy problem need be solved; as these are uncoupled, they can be solved in parallel. The unconditional stability and convergence of the first method is proved and also illustrated through numerical experiments. The improved temporal convergence and unconditional stability of the second method is also illustrated through numerical experiments.
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Additional Information
  • Yanzhao Cao
  • Affiliation: Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36830
  • Email:
  • Max Gunzburger
  • Affiliation: Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306
  • MR Author ID: 78360
  • Email:
  • Xiaoming He
  • Affiliation: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Missouri 65409
  • Email:
  • Xiaoming Wang
  • Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
  • Email:
  • Received by editor(s): June 7, 2010
  • Received by editor(s) in revised form: July 22, 2012
  • Published electronically: February 3, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 1617-1644
  • MSC (2010): Primary 65M55, 65M12, 65M15, 65M60, 35M10, 35Q35, 76D07, 76S05
  • DOI:
  • MathSciNet review: 3194124