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A Fictitious-Domain Method with Distributed Multiplier for the Stokes Problem

In: Applied Nonlinear Analysis

Author

Listed:
  • Vivette Girault
  • Roland Glowinski
  • T. W. Pan

Abstract

This article is devoted to the numerical analysis of a fictitious domain method for the Stokes problem, where the boundary condition is enforced weakly by means of a multiplier defined in a portion of the domain. In practice, this is applied for example to the sedimentation of many particles in a fluid. It is found that the multiplier is divergence-free. We present here sufficient conditions on the relative mesh sizes for convergence of the discrete method. Also, we show how the constraint on the divergence of the discrete multiplier can be relaxed when such a sedimentation problem is discretized.

Suggested Citation

  • Vivette Girault & Roland Glowinski & T. W. Pan, 2002. "A Fictitious-Domain Method with Distributed Multiplier for the Stokes Problem," Springer Books, in: Adélia Sequeira & Hugo Beirão da Veiga & Juha Hans Videman (ed.), Applied Nonlinear Analysis, pages 159-174, Springer.
    • Handle: RePEc:spr:sprchp:978-0-306-47096-7_12
    DOI: 10.1007/0-306-47096-9_12
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