Convergence behaviour of defect correction for hyperbolic equations

Abstract In this note we present results about the convergence rate of a defect correction process for the solution of second-order accurate convection problems. The operator to be inverted is a stable, first-order accurate discretisation. It is shown how the choice of the second-order discretisation scheme influences the convergence rate. Neither the second-order unwind, nor the central scheme converge, but intermediate schemes do.