4. Order 2 extension

Finite volume schemes are by construction of order 1 in space, i.e. they approximate the exact equation in O (h). For problems dominated by transport, or at least in which transport plays a decisive role, experience shows that order 1 is largely insufficient. In practice, excessive numerical scattering is added to the scattering of physical origin. Consider the coupled problem in section 1.2.5 . For constant coefficients in space, we can...