Geodesic
Boundary augmented Lagrangian method for the Signorini problem
Applications of Mathematics, Tome 61 (2016) no. 2, pp. 215-231
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An augmented Lagrangian method, based on boundary variational formulations and fixed point method, is designed and analyzed for the Signorini problem of the Laplacian. Using the equivalence between Signorini boundary conditions and a fixed-point problem, we develop a new iterative algorithm that formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Both theoretical results and numerical experiments show that the method presented is efficient.
An augmented Lagrangian method, based on boundary variational formulations and fixed point method, is designed and analyzed for the Signorini problem of the Laplacian. Using the equivalence between Signorini boundary conditions and a fixed-point problem, we develop a new iterative algorithm that formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Both theoretical results and numerical experiments show that the method presented is efficient.
DOI : 10.1007/s10492-016-0129-7
Classification : 35J05, 35J58, 65N38
Keywords: Signorini problem; augmented Lagrangian; fixed point; Steklov-Poincaré operator; boundary integral equation 
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     title = {Boundary augmented {Lagrangian} method for the {Signorini} problem},
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Zhang, Shougui; Li, Xiaolin. Boundary augmented Lagrangian method for the Signorini problem. Applications of Mathematics, Tome 61 (2016) no. 2, pp. 215-231. doi: 10.1007/s10492-016-0129-7

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