Overlapping Domain Decomposition Methods for Noncoercive Hamilton-Jacobi-Bellman Equation

This study presents an approach to demonstrate the monotonic and geometric convergence of the non-coercive Hamilton-Jacobi-Bellman problem with Dirichlet boundary conditions using the finite difference method. The approach combines overlapping domain decomposition with a sequence of lower and upper solutions to characterize the solution in a discrete setting. Numerical experiments are conducted to validate the methodology and illustrate the consistency of the theoretical findings.