Jaroszkowski, B;
Jensen, M;
(2022)
Finite Element Methods for Isotropic Isaacs Equations with Viscosity and Strong Dirichlet Boundary Conditions.
Applied Mathematics and Optimization
, 85
(2)
, Article 8. 10.1007/s00245-022-09860-5.
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Abstract
We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic game theory and optimal control and show uniform convergence to the viscosity solution. Elliptic projections are used to manage singular behaviour at the boundary and to treat a violation of the consistency conditions from the framework by Barles and Souganidis by the numerical operators. Boundary conditions may be imposed in the viscosity or in the strong sense, or in a combination thereof. The presented monotone numerical method has well-posed finite dimensional systems, which can be solved efficiently with Howard’s method.
| Type: | Article |
|---|---|
| Title: | Finite Element Methods for Isotropic Isaacs Equations with Viscosity and Strong Dirichlet Boundary Conditions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00245-022-09860-5 |
| Publisher version: | https://doi.org/10.1007/s00245-022-09860-5 |
| Language: | English |
| Additional information: | © 2022 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Finite element methods, Isaacs equations, Bellman equations, Fully nonlinear, Viscosity solution, Boundary conditions |
| UCL classification: | 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 UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10156972 |
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