On the order of accuracy of edge-based schemes on meshes of a special type

Unsteady corrector method proposed earlier by the author is applied to estimate the accuracy of several edge-based schemes for the transport equation with constant velocity. Second order of accuracy on block refinement is proved. Fractional order of accuracy is obtained on meshes with constant element quality. For a special type of meshes we prove the $5/4$ order of accuracy in $L_\infty$ norm for EBR3 scheme and demonstrate that this estimate can’t be improved.