Mixed finite-element methods for Hamilton–Jacobi–Bellman-type equations

The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first- and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L² are demonstrated for the relevant functions. Error estimates are also derived in L^q, 2≤q≤+∞