A New Approach to Asymptotic Behavior for a Finite Element Approximation in Parabolic Variational Inequalities

Abstract EN

The paper deals with the theta time scheme combined with a finite element spatial approximation of parabolic variational inequalities.

The parabolic variational inequalities are transformed into noncoercive elliptic variational inequalities.

A simple result to time energy behavior is proved, and a new iterative discrete algorithm is proposed to show the existence and uniqueness.

Moreover, its convergence is established.

Furthermore, a simple proof to asymptotic behavior in uniform norm is given.