931 research outputs found

    An a posteriori error estimate for Symplectic Euler approximation of optimal control problems

    Get PDF
    This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests

    Self-Adaptive Methods for PDE

    Get PDF
    [no abstract available

    Adaptive C\u3csup\u3e0\u3c/sup\u3e interior penalty methods for Hamilton–Jacobi–Bellman equations with Cordes coefficients

    Get PDF
    In this paper we conduct a priori and a posteriori error analysis of the C interior penalty method for Hamilton–Jacobi–Bellman equations, with coefficients that satisfy the Cordes condition. These estimates show the quasi-optimality of the method, and provide one with an adaptive finite element method. In accordance with the proven regularity theory, we only assume that the solution of the Hamilton–Jacobi–Bellman equation belongs to H . 0

    Adaptive interior penalty methods for Hamilton–Jacobi–Bellman equations with Cordes coefficients

    Get PDF
    In this paper we conduct a priori and a posteriori error analysis of the C0 interior penalty method for Hamilton–Jacobi–Bellman equations, with coefficients that satisfy the Cordes condition. These estimates show the quasi-optimality of the method, and provide one with an adaptive finite element method. In accordance with the proven regularity theory, we only assume that the solution of the Hamilton–Jacobi–Bellman equation belongs to H2
    • …
    corecore