Jaroszkowski, Bartosz;
Jensen, Max;
(2023)
Finite element approximation of Hamilton–Jacobi–Bellman equations with nonlinear mixed boundary conditions.
IMA Journal of Numerical Analysis
, Article drad013. 10.1093/imanum/drad013.
(In press).
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Abstract
We show strong uniform convergence of monotone P1 finite element methods to the viscosity solution of isotropic parabolic Hamilton–Jacobi–Bellman equations with mixed boundary conditions on unstructured meshes and for possibly degenerate diffusions. Boundary operators can generally be discontinuous across face-boundaries and type changes. Robin-type boundary conditions are discretized via a lower Dini derivative. In time, the Bellman equation is approximated through IMEX schemes. Existence and uniqueness of numerical solutions follows through Howard’s algorithm.
| Type: | Article |
|---|---|
| Title: | Finite element approximation of Hamilton–Jacobi–Bellman equations with nonlinear mixed boundary conditions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/drad013 |
| Publisher version: | https://doi.org/10.1093/imanum/drad013 |
| Language: | English |
| Additional information: | © The Author(s) 2023. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | finite element methods; Hamilton–Jacobi–Bellman equations; mixed boundary conditions; fully nonlinear equations; viscosity solutions. |
| 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-pp.ucl.ac.uk/id/eprint/10165977 |
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