In this paper, a general high-order multi-domain hybrid DG/WENO-FDmethod, which couples a p-order (p ≥ 3) DG method and a q-order (q ≥ 3) WENO-FD scheme, is developed. There are two possible coupling approaches at the domain interface, one is non-conservative, the other is conservative. The non-conservative coupling approach can preserve optimal order of accuracy and the local conservative erro...