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

• Main Authors: Mohamed Amine Bencheikh Le Hocine, Salah Boulaaras, Mohamed Haiour
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-12-01
• Series: Cogent Mathematics
• Subjects: parabolic quasi-variational inequalities; Hamilton–Jacobi–Bellman equation; finite element methods; subsolutions method; $ L^{\infty } $-asymptotic behavior; asymptotic behavior; orthogonal polynomials and special functions
• Online Access: http://dx.doi.org/10.1080/23311835.2016.1251386
• ISSN: 2331-1835

In this paper, an optimal error estimate for system of parabolic quasi-variational 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^{\infty } $-asymptotic behavior in maximum norm is proved using the semi-implicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolution and discrete regularity.