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

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.

### 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
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### References:

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