Abstract: With study of finite volume(FV) methods and discontinuous Galerkin(DG) method,"static reconstruction" and "dynamic reconstruction" are proposed for high-order numerical schemes.Based on the concept of "hybrid reconstruction",a new class of hybrid DG/FV schemes is presented for two-dimensional(2D) unstructured grids to solve the 2D conservation law,including 2D scalar equations and Euler equations.In the hybrid DG/FV schemes,lower-order derivatives of the piecewise polynomial are computed locally in a cell by a traditional DG method(called "dynamic reconstruction"),and the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method by using lower-order derivatives in the cell and immediate neighbour cells.Typical 2D cases are given,and accuracy study is carried out.Numerical results show that the hybrid DG/FV scheme reaches desired order of accuracy.In addition,the hybrid DG/FV scheme saves great CPU time and memory compared with same order DG schemes.

Key words: discontinuous Galerkin method, finite volume method, Taylor basis, hybrid scheme, unstructured grids