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Fictitious domain formulations of unilateral problems: analysis and algorithms

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Abstract

The present article deals with fictitious domain methods for numerical realization of scalar variational inequalities with the Signorini type conditions on the boundary. Two variants are introduced and analyzed. A discretization is done by finite elements. It leads to a system of non-smooth, piecewise linear equations. This system is solved by the semismooth Newton method. Numerical experiments confirm the efficiency of this approach.

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Authors and Affiliations

  1. Department of Numerical Mathematics, Charles University, Prague, Czech Republic

    J. Haslinger

  2. Department of Applied Mathematics, VŠB-Technical University, Ostrava, Czech Republic

    T. Kozubek & R. Kučera

Authors
  1. J. Haslinger
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  2. T. Kozubek
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  3. R. Kučera
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Correspondence to T. Kozubek.

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Haslinger, J., Kozubek, T. & Kučera, R. Fictitious domain formulations of unilateral problems: analysis and algorithms. Computing 84, 69–96 (2009). https://doi.org/10.1007/s00607-009-0026-y

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  • DOI: https://doi.org/10.1007/s00607-009-0026-y

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