The Effect of Quadrature on the Convergence of Policy Iteration for Hamilton–Jacobi–Bellman Equations

Modern finite element libraries allow users to express partial differential equations directly in variational form, with the added convenience of automatic quadrature selection. In the context of Hamilton–Jacobi–Bellman (HJB) equations, automatic quadrature selection can result in nonmatching quadratures between different terms that may lead to loss of convergence of the policy iteration, which is otherwise expected from theory to converge superlinearly. The simple remedy of enforcing matching quadrature recovers the expected superlinear convergence.