Advective transport via error minimization: Enforcing constraints of non- negativity and conservation (Q1086502)

An operations research method is presented for deriving a conservative, non-negative computational scheme for advective transport. Finite elements in space and time are used to approximate the solution, and the integral of the square of the residual is minimized over the entire spatial domain and over a single temporal element. Negative values are excluded by inequality constraints and conservation is enforced by Lagrange multipliers. The method is then generalized to show how negative values arising in conventional finite-difference methods can be eliminated.