Modelling material properties in high-order compact schemes

High-order compact-difference methods have been applied to a variety of physical phenomenon, including modelling Maxwell´s equations. Proper treatment at material interfaces is difficult for high-order schemes, as the derivatives of the primitive variables are discontinuous across the interface. Similar situations occur in attempting to use compact-differences in fluid dynamic problems containing shock waves. In the fluids community the problem has been dealt with by dropping to a second-order scheme at the discontinuity. With Maxwell´s equations, the stationary location of the material interface and the behaviour of the derivatives at that interface allow for higher-order formulations of the problem. Details of the treatment of material interfaces that preserve the formal order of accuracy for computing the derivatives and filtering the solutions are presented and discussed.