Evolutionary Variational Inequalities with Viscosity

2009 ◽  
pp. 1-14 ◽  
Author(s):  
Mircea Sofonea ◽  
Andaluzia Matei
Keyword(s):  
Variational Inequalities ◽  
Evolutionary Variational Inequalities

A CLASS OF EVOLUTIONARY VARIATIONAL INEQUALITIES WITH VOLTERRA-TYPE TERM

2004 ◽  
Vol 14 (04) ◽  
pp. 557-577 ◽  
Author(s):  
A. RODRÍGUEZ-ARÓS ◽  
J. M. VIAÑO ◽  
M. SOFONEA
Keyword(s):  
Variational Inequalities ◽  
Numerical Approximation ◽  
Contact Problems ◽  
Uniqueness Result ◽  
Long Term Memory ◽  
Term Memory ◽  
Frictionless Contact ◽  
Fully Discrete ◽  
Evolutionary Variational Inequalities

We consider a class of abstract evolutionary variational inequalities arising in the study of frictionless contact problems for linear viscoelastic materials with long-term memory. We prove an existence and uniqueness result, by using arguments of time-dependent elliptic variational inequalities and Banach's fixed point theorem. We then consider numerical approximation of the problem by introducing spatially semi-discrete, time semi-discrete and fully discrete schemes. For both schemes, we show the existence of a unique solution and derive error estimates. Finally, we apply the abstract results to the analysis and numerical approximation of the Signorini frictionless contact problem between two viscoelastic bodies with long-term memory.

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