2021/05/20 by Bartosz Jaroszkowski, Max Jensen, Jaroszkowski, Bartosz +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2105.09585
openalex publication_date 2021/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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