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    A Nonoverlapping Domain Decomposition Method for Incompressible Stokes Equations with Continuous Pressures

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    Issue Date
    2013
    Author
    Li, Jing
    Tu, Xuemin
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    A nonoverlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressure component is enforced in the primal form, i.e., neighboring subdomains share the same pressure degrees of freedom on the subdomain interface and no Lagrange multipliers are needed. After eliminating all velocity variables and the independent subdomain interior parts of the pressures, a symmetric positive semidefinite linear system for the subdomain boundary pressures and the Lagrange multipliers is formed and solved by a preconditioned conjugate gradient method. A lumped preconditioner is studied and the condition number bound of the preconditioned operator is proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments demonstrate the convergence rate of the proposed algorithm.
    Description
    This is the publisher's version, also available electronically from http://epubs.siam.org/doi/abs/10.1137/120861503
    URI
    http://hdl.handle.net/1808/14626
    DOI
    https://doi.org/10.1137/120861503
    ISSN
    0036-1429
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Jing Li, Xuemin Tu. (2013). A non-overlapping domain decomposition method for incompressible Stokes equations with continuous pressures. SIAM Journal on Numerical Analysis 51:1235-1253. http://www.dx.doi.org/10.1137/120861503

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    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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