A penalty method for history-dependent variational-hemivariational inequalities

作者：Sofonea Mircea; Migorski Stanislaw^*; Han Weimin

来源：Computers & Mathematics with Applications, 2018, 75(7): 2561-2573.

DOI：10.1016/j.camwa.2017.12.018

• History-dependent operator
• Penalty method
• Existence and uniqueness
• Convergence
• Contact Mechanics

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.

• 出版日期2018-4-1