Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity

Finite-difference approximations to an elliptic-hyperbolic system arising in vortex density models for type II superconductors are studied. The problem can be formulated as a non-local Hamilton-Jacobi equation on a bounded domain with zero Neumann boundary conditions. Monotone schemes are defined and shown to be stable. An L{infty} error bound is proved for the approximations of the unique viscosity solution.