Finite Element Approximation of Hamilton-Jacobi-Bellman equations with nonlinear mixed boundary conditions
Numerical Analysis
2021-05-21 v1 Numerical Analysis
Optimization and Control
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 discretised 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. Keywords: Finite element method, Hamilton-Jacobi-Bellman equation, Mixed boundary conditions, Fully nonlinear equation, Viscosity solution
Keywords
Cite
@article{arxiv.2105.09585,
title = {Finite Element Approximation of Hamilton-Jacobi-Bellman equations with nonlinear mixed boundary conditions},
author = {Bartosz Jaroszkowski and Max Jensen},
journal= {arXiv preprint arXiv:2105.09585},
year = {2021}
}