A nonoverlapping domain decomposition method for variational inequalities derived from free boundary problems

  1. Bin Jiang1,*,
  2. John C. Bruch Jr.2,3,
  3. James M. Sloss3

Article first published online: 20 APR 2005

DOI: 10.1002/num.20083

Issue

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations

Volume 22, Issue 1, pages 1–17, January 2006

Additional Information

How to Cite

Jiang, B., Bruch, J. C. and Sloss, J. M. (2006), A nonoverlapping domain decomposition method for variational inequalities derived from free boundary problems. Numerical Methods for Partial Differential Equations, 22: 1–17. doi: 10.1002/num.20083

Author Information

  1. 1

    Department of Mathematics and Statistics, Portland State University, Portland, Oregon 97207

  2. 2

    Departments of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106

  3. 3

    Department of Mathematics, University of California, Santa Barbara, CA 93106

*Department of Mathematics and Statistics, Portland State University, Portland, OR 97207

Publication History

  1. Issue published online: 27 OCT 2005
  2. Article first published online: 20 APR 2005
  3. Manuscript Accepted: 28 FEB 2005
  4. Manuscript Received: 3 MAY 2004

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Keywords:

  • domain decomposition;
  • variational inequality;
  • fixed domain;
  • free surface seepage

Abstract

The article proposes a nonoverlapping domain decomposition method for variational inequalities derived from free boundary problems. The free boundary value problem is broken up into two problems on nonoverlapping regions. In one region the problem is treated as a partial differential equation, while in the second region that contains the free boundary part, a variational inequality is considered. By solving these two related problems successively, we have shown that the successive solutions converge to the solution of the original problem. Application to a free surface seepage problem is given. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006

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