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 (Formula presented.) -refinement.
CITATION STYLE
Smears, I., & Süli, E. (2016). Discontinuous Galerkin finite element methods for time-dependent Hamilton–Jacobi–Bellman equations with Cordes coefficients. Numerische Mathematik, 133(1), 141–176. https://doi.org/10.1007/s00211-015-0741-6
Mendeley helps you to discover research relevant for your work.