Finite-Element Discretization and Error Bounds in Dynamical Systems for Traffic Flow Optimization in South Africa

Finite-element discretization methods are widely used in solving partial differential equations (PDEs), which describe dynamical systems governing traffic flow optimization. A mathematical model based on PDEs will be discretized using the finite-element method, with assumptions about traffic dynamics and network characteristics. This framework provides a robust theoretical basis for understanding and optimising traffic flow dynamics on South African roads using numerical methods. Further research should validate these findings with empirical data from real-world traffic scenarios. Model selection is formalised as θ̂=argminθ∈Θ(θ)+λ\,Ω(θ)\ with consistency under mild identifiability assumptions.