A multigrid optimization algorithm for the numerical solution of quasilinear variational inequalities involving the p-Laplacian

In this paper we propose a multigrid optimization algorithm (MG/OPT) for the numerical solution of a class of quasilinear variational inequalities of the second kind. This approach is enabled by the fact that the solution of the variational inequality is given by the minimizer of a nonsmooth energy...

Full description

Saved in:
Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2018-02, Vol.75 (4), p.1107-1127
Main Authors: González-Andrade, Sergio, López-Ordóñez, Sofía
Format: Article
Language:English
Subjects:
[formula omitted]-Laplacian
Algorithms
Computational fluid dynamics
Computer simulation
Convergence
Discretization
Finite element analysis
Finite element method
Fluid flow
Fluid mechanics
Inequalities
Laplace transforms
Mathematical analysis
Multigrid methods
Numerical analysis
Optimization
Optimization algorithms
Preconditioned descent algorithms
Regularity
Regularization
Studies
Variational inequalities of the second kind
Viscoplastic fluids
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we propose a multigrid optimization algorithm (MG/OPT) for the numerical solution of a class of quasilinear variational inequalities of the second kind. This approach is enabled by the fact that the solution of the variational inequality is given by the minimizer of a nonsmooth energy functional, involving the p-Laplace operator. We propose a Huber regularization of the functional and a finite element discretization for the problem. Further, we analyze the regularity of the discretized energy functional, and we are able to prove that its Jacobian is slantly differentiable. This regularity property is useful to analyze the convergence of the MG/OPT algorithm. In fact, we demonstrate that the algorithm is globally convergent by using a mean value theorem for semismooth functions. Finally, we apply the MG/OPT algorithm to the numerical simulation of the viscoplastic flow of Bingham, Casson and Herschel–Bulkley fluids in a pipe. Several experiments are carried out to show the efficiency of the proposed algorithm when solving this kind of fluid mechanics problems.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.10.027