On a Fictitious Domain Method for Unilateral Problems

J. Haslinger (), T. Kozubek () and R. Kučera ()
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J. Haslinger: Charles University
T. Kozubek: VŠB-TU Ostrava
R. Kučera: VŠB-TU Ostrava

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 803-810 from Springer

Abstract: 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.

Keywords: Newton Method; Newton Iteration; Domain Formulation; Superlinear Convergence; Semismooth Newton Method (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_96

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DOI: 10.1007/978-3-540-69777-0_96

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