In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton- Jacobi-Bellman equation (HJB) with noncoercive operators. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart, and then between the continuous solution and the approximate solution.
Digital Object Identifier (DOI)
Miloudi, M.; Saadi, S.; and Haiour, M.
"Hamilton-Jacobi-Bellman Equations: An Algorithmic Contraction New Approach,"
Applied Mathematics & Information Sciences: Vol. 15
, Article 10.
Available at: https://dc.naturalspublishing.com/amis/vol15/iss1/10