UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Discontinuous Galerkin finite element methods for time-dependent Hamilton-Jacobi-Bellman equations with Cordes coefficients

Smears, I; Sueli, E; (2016) Discontinuous Galerkin finite element methods for time-dependent Hamilton-Jacobi-Bellman equations with Cordes coefficients. Numerische Mathematik , 133 (1) pp. 141-176. 10.1007/s00211-015-0741-6. Green open access

[thumbnail of DG Parabolic HJB.pdf]
Preview
Text
DG Parabolic HJB.pdf - Accepted Version

Download (404kB) | Preview

Abstract

We propose and analyse a fully discrete discontinuous Galerkin time-stepping method for parabolic Hamilton–Jacobi–Bellman equations with Cordes coefficients. The method is consistent and unconditionally stable on rather general unstructured meshes and time-partitions. Error bounds for both rough and regular solutions in terms of temporal regularity show that the method is arbitrarily high-order with optimal convergence rates with respect to the mesh size, time-interval length and temporal polynomial degree, and possibly suboptimal by an order and a half in the spatial polynomial degree. Numerical experiments on problems with strongly anisotropic diffusion coefficients and early-time singularities demonstrate the accuracy and computational efficiency of the method, with exponential convergence rates achieved under combined hp- and τq-refinement.

Type: Article
Title: Discontinuous Galerkin finite element methods for time-dependent Hamilton-Jacobi-Bellman equations with Cordes coefficients
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-015-0741-6
Publisher version: https://doi.org/10.1007/s00211-015-0741-6
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Fully nonlinear partial differential equations, Hamilton–Jacobi–Bellman equations, hp-version discontinuous Galerkin methods, Cordes condition
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1572502
Downloads since deposit
Loading...
116Downloads
Download activity - last month
Loading...
Download activity - last 12 months
Loading...
Downloads by country - last 12 months
Loading...

Archive Staff Only

View Item View Item