On finite element approximation of system of parabolic quasi-variational inequalities related to stochastic control problems

Abstract: In this paper, an optimal error estimate for system of parabolic quasivariational inequalities related to stochastic control problems is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L ∞ -asymptotic behavior in maximum norm is proved using the semiimplicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolution and discrete regularity