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On a Fictitious Domain Method for Unilateral Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • J. Haslinger

    (Charles University)

  • T. Kozubek

    (VŠB-TU Ostrava)

  • R. Kučera

    (VŠB-TU Ostrava)

Abstract

Two variants of the fictitious domain method are compared. The first one enforces unilateral conditions by Langrange multipliers defined on the boundary γ of the original domain ω so that the computed solution has a singularity on γ that can result in an intrinsic error. The second one uses an auxiliary boundary Γ located outside of $$\overline{\omega}$$ on which a new control variable is introduced in order to satisfy the conditions on γ. Therefore the singularity is moved away from $$\overline{\omega}$$ so that the computed solution is smoother in ω. It is experimentally shown that the discretization error is significantly smaller in this case.

Suggested Citation

  • J. Haslinger & T. Kozubek & R. Kučera, 2008. "On a Fictitious Domain Method for Unilateral Problems," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 803-810, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_96
    DOI: 10.1007/978-3-540-69777-0_96
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