The Mathematical Institute, University of Oxford, Eprints Archive

Discontinuous Galerkin finite element approximation of Hamilton-Jacobi-Bellman equations with Cordès coefficients

Smears, Iain and Suli, Endre (2013) Discontinuous Galerkin finite element approximation of Hamilton-Jacobi-Bellman equations with Cordès coefficients. Technical Report. Unspecified. (Submitted)

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Abstract

We propose an hp-version discontinuous Galerkin finite element method for fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman equations with Cord�ès 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 strongly anisotropic diffusion coefficients illustrate the accuracy and computational efficiency of the scheme. An existence and uniqueness result for strong solutions of the fully nonlinear problem, and a semismoothness result for the nonlinear operator are also provided.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Partial differential equations
O - Z > Operator theory
A - C > Calculus of variations and optimal control
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1671
Deposited By: Lotti Ekert
Deposited On:22 Feb 2013 09:55
Last Modified:29 May 2015 19:21

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