Jensen, M;
Smears, I;
(2013)
On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations.
SIAM: Journal on Numerical Analysis
, 51
(1)
pp. 137-162.
10.1137/110856198.
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Abstract
We study the convergence of monotone $P1$ finite element methods on unstructured meshes for fully nonlinear Hamilton--Jacobi--Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic diffusions. Using elliptic projection operators we treat discretizations which violate the consistency conditions of the framework by Barles and Souganidis. We obtain strong uniform convergence of the numerical solutions and, under nondegeneracy assumptions, strong $L^2$ convergence of the gradients.
| Type: | Article |
|---|---|
| Title: | On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/110856198 |
| Publisher version: | http://dx.doi.org/10.1137/110856198 |
| Language: | English |
| Additional information: | © 2013, Society for Industrial and Applied Mathematics 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, finite element methods, partial differential equations, Hamilton-Jacobi-Bellman equations, viscosity solutions, PARTIAL-DIFFERENTIAL EQUATIONS, DISCRETE MAXIMUM PRINCIPLE, PARABOLIC EQUATIONS, VISCOSITY SOLUTIONS, APPROXIMATION, DIFFUSION, SCHEMES, COEFFICIENTS, GRIDS, TIME |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices 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/1572496 |
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