Smears, I;
Sueli, E;
(2014)
Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients.
SIAM Journal on Numerical Analysis
, 52
(2)
pp. 993-1016.
10.1137/130909536.
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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 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 nonsmooth solutions and 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.
| Type: | Article |
|---|---|
| Title: | Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/130909536 |
| Publisher version: | https://doi.org/10.1137/130909536 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Hamilton-Jacobi-Bellman equations, hp-version discontinuous Galerkin finite element methods, Cordes condition, fully nonlinear equations, semismooth Newton methods, PARTIAL-DIFFERENTIAL-EQUATIONS, ELLIPTIC-EQUATIONS, PARABOLIC EQUATIONS, VISCOSITY SOLUTIONS, CONVERGENCE, 2ND-ORDER, SCHEMES |
| 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/1572507 |
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