A preconditioned descent algorithm for variational inequalities of the second kind involving the p-Laplacian operator

This paper is concerned with the numerical solution of a class of variational inequalities of the second kind, involving the p -Laplacian operator. This kind of problems arise, for instance, in the mathematical modelling of non-Newtonian fluids. We study these problems by using a regularization appr...

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Bibliographic Details
Published in:Computational optimization and applications 2017, Vol.66 (1), p.123-162
Main Author: González-Andrade, Sergio
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convergence
Convex and Discrete Geometry
Descent
Inequalities
Management Science
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Numerical analysis
Operations Research
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Polynomials
Statistics
Studies
Variational methods
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Summary:This paper is concerned with the numerical solution of a class of variational inequalities of the second kind, involving the p -Laplacian operator. This kind of problems arise, for instance, in the mathematical modelling of non-Newtonian fluids. We study these problems by using a regularization approach, based on a Huber smoothing process. Well posedness of the regularized problems is proved, and convergence of the regularized solutions to the solution of the original problem is verified. We propose a preconditioned descent method for the numerical solution of these problems and analyze the convergence of this method in function spaces. The existence of admissible descent directions is established by variational methods and admissible steps are obtained by a backtracking algorithm which approximates the objective functional by polynomial models. Finally, several numerical experiments are carried out to show the efficiency of the methodology here introduced.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-016-9861-x