A penalty method for history-dependent variational–hemivariational inequalities

Penalty methods approximate a constrained variational or hemivariational inequality problem through a sequence of unconstrained ones as the penalty parameter approaches zero. The methods are useful in the numerical solution of constrained problems, and they are also useful as a tool in proving solut...

Full description

Saved in:
Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2018-04, Vol.75 (7), p.2561-2573
Main Authors: Sofonea, Mircea, Migórski, Stanisław, Han, Weimin
Format: Article
Language:English
Subjects:
Approximation
Contact Mechanics
Convergence
Existence and uniqueness
History-dependent operator
Inequalities
Inequality
Mathematical models
Mathematics
Operators (mathematics)
Parameters
Penalty method
Viscoelasticity
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:Penalty methods approximate a constrained variational or hemivariational inequality problem through a sequence of unconstrained ones as the penalty parameter approaches zero. The methods are useful in the numerical solution of constrained problems, and they are also useful as a tool in proving solution existence of constrained problems. This paper is devoted to a theoretical analysis of penalty methods for a general class of variational–hemivariational inequalities with history-dependent operators. Unique solvability of penalized problems is shown, as well as the convergence of their solutions to the solution of the original history-dependent variational–hemivariational inequality as the penalty parameter tends to zero. The convergence result proved here generalizes several existing convergence results of penalty methods. Finally, the theoretical results are applied to examples of history-dependent variational–hemivariational inequalities in mathematical models describing the quasistatic contact between a viscoelastic rod and a reactive foundation.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.12.018