The finite element approximation of Hamilton-Jacobi-Bellman equations: the noncoercive case
نویسندگان
چکیده
This paper deals with the finite element approximation of Hamilton-Jacobi-Bellman equations. We establish a convergence and a quasi-optimal Lm -error estimate, involving a weakly coupled system of quasi-variational inequalities for the solution of which an iterative scheme of monotone kind is introduced and analyzed.
منابع مشابه
Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients | SIAM Journal on Numerical Analysis | Vol. 52, No. 2 | Society for Industrial and Applied Mathematics
We propose an hp-version discontinuous Galerkin finite element method for fully nonlinear second-order elliptic Hamilton–Jacobi–Bellman equations with Cordes coefficients. The method is proved to be consistent and stable, with convergence rates that are optimal with respect to mesh size, and suboptimal in the polynomial degree by only half an order. Numerical experiments on problems with nonsmo...
متن کاملDiscontinuous Galerkin Finite Element Approximation of Hamilton-Jacobi-Bellman Equations with Cordes Coefficients
We propose an hp-version discontinuous Galerkin finite element method for fully nonlinear second-order elliptic Hamilton–Jacobi–Bellman equations with Cordès coefficients. The method is proven to be consistent and stable, with convergence rates that are optimal with respect to mesh size, and suboptimal in the polynomial degree by only half an order. Numerical experiments on problems with strong...
متن کاملHamilton-Jacobi-Bellman Equations
This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...
متن کاملError bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general results to various schemes including finite difference schemes, splitting methods and the classical approximation by piecewise constant controls.
متن کاملNonlinear HJB Equations
This paper is concerned with the standard finite element approximation of HamiltonJacobi-Bellman Equations (HJB) with nonlinear source terms. Under a realistic condition on the nonlinearity, we characterize the discrete solution as a fixed point of a contraction. As a result of this, we also derive a sharp L∞error estimate of the approximation. Mathematics Subject Classification: Primary 35F21;...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Applied Mathematics and Computation
دوره 158 شماره
صفحات -
تاریخ انتشار 2004