931 research outputs found
An a posteriori error estimate for Symplectic Euler approximation of optimal control problems
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
[no abstract available
Adaptive C\u3csup\u3e0\u3c/sup\u3e interior penalty methods for Hamilton–Jacobi–Bellman equations with Cordes coefficients
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
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
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