2014/12/19 by Mariela C. Olguín, Olguín, Mariela, Domingo A. Tarzia +1
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.1412.6500
A continuous optimal control problem governed by an elliptic variational\ninequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53\n(2012), 375-392 where the control variable is the internal energy g. It was\nproved the existence and uniqueness of the optimal control and its associated\nstate system. The objective of this work is to make the numerical analysis of\nthe above optimal control problem, through the finite element method with\nLagrange's triangles of type 1. We discretize the elliptic variational\ninequality which define the state system and the corresponding cost functional,\nand we prove that there exists a discrete optimal control and its associated\ndiscrete state system for each positive h (the parameter of the finite\nelement method approximation). Finally, we show that the discrete optimal\ncontrol and its associated state system converge to the continuous optimal\ncontrol and its associated state system when the parameter h goes to zero.\n