A new error estimate on uniform norm of a parabolic variational inequality with nonlinear source terms via the subsolution concepts

This paper deals with the numerical analysis of parabolic variational inequalities with nonlinear source terms, where the existence and uniqueness of the solution is provided by using Banach’s fixed point theorem. In addition, an optimally L ∞ -asymptotic behavior is proved using Euler time scheme combined with the finite element spatial approximation. The approach is based on Bensoussan–Lions algorithm for evolutionary free boundary problems using the concepts of subsolutions.