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Numerische Mathematik

, Volume 133, Issue 1, pp 141–176 | Cite as

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

  • Iain SmearsEmail author
  • Endre Süli
Article

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 \(\tau q\)-refinement.

Mathematics Subject Classification

65N30 65N12 65N15 35K10 35K55 35D35 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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