Journal of the
Korean Mathematical Society JKMS

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the {\em Cell Boundary Element} (CBE) method, which is the finite element type flux preserving methods.

Keywords: cell boundary element method, optimal control problem, Gauss-Seidel iteration

MSC numbers: 65M55, 65N30