2000 character limit reached
Finite Element Approximation of Hamilton-Jacobi-Bellman equations with nonlinear mixed boundary conditions (2105.09585v1)
Published 20 May 2021 in math.NA, cs.NA, and math.OC
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