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Zhang, Shougui; Li, Xiaolin

Boundary augmented Lagrangian method for the Signorini problem. (English) Zbl 1389.35164

Appl. Math., Praha 61, No. 2, 215-231 (2016).
In this article, the authors consider an augmented Lagrangian method that is based on (i) a boundary variational formulation and (ii) a fixed point method. This boundary augmented Lagrangian method is specifically designed and analyzed for the Signorini problem of the Laplacian. The authors develop a new iterative scheme using the equivalence between the Signorini boundary conditions and a fixed-point problem. It formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Finally, it is shown by theoretical and numerical results that the novel method is efficient.
Reviewer: Andreas Kleefeld (Jülich)

Cited in 1 Document

MSC:

35J58 Boundary value problems for higher-order elliptic systems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N38 Boundary element methods for boundary value problems involving PDEs

Keywords:

Signorini problem; augmented Lagrangian; fixed point; Steklov-Poincaré operator; boundary integral equation
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\textit{S. Zhang} and \textit{X. Li}, Appl. Math., Praha 61, No. 2, 215--231 (2016; Zbl 1389.35164)
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