Unsteady corrector method for accuracy analysis of linear numerical schemes for transport equation

We introduce the concept of unsteady corrector for a wide class of linear numerical schemes for the transport equation with constant velocity on non-uniform and unstructured meshes. The unsteady corrector is governed by the same equation as the numerical solution but with nonzero right-hand side. We show that its analysis allows to obtain supraconvergence and long-time simulation accuracy properties.