Boundary augmented Lagrangian method for the Signorini problem

Shougui Zhang; Xiaolin Li

Applications of Mathematics (2016)

  • Volume: 61, Issue: 2, page 215-231
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Zhang, Shougui, and Li, Xiaolin. "Boundary augmented Lagrangian method for the Signorini problem." Applications of Mathematics 61.2 (2016): 215-231. <http://eudml.org/doc/276774>.

@article{Zhang2016,
abstract = {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.},
author = {Zhang, Shougui, Li, Xiaolin},
journal = {Applications of Mathematics},
keywords = {Signorini problem; augmented Lagrangian; fixed point; Steklov-Poincaré operator; boundary integral equation; Signorini problem; augmented Lagrangian; fixed point; Steklov-Poincaré operator; boundary integral equation},
language = {eng},
number = {2},
pages = {215-231},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundary augmented Lagrangian method for the Signorini problem},
url = {http://eudml.org/doc/276774},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Zhang, Shougui
AU - Li, Xiaolin
TI - Boundary augmented Lagrangian method for the Signorini problem
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 215
EP - 231
AB - 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.
LA - eng
KW - Signorini problem; augmented Lagrangian; fixed point; Steklov-Poincaré operator; boundary integral equation; Signorini problem; augmented Lagrangian; fixed point; Steklov-Poincaré operator; boundary integral equation
UR - http://eudml.org/doc/276774
ER -

References

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