The high order control volume discontinuous Petrov–Galerkin finite element method for the hyperbolic conservation laws based on Lax–Wendroff time discretization

In this paper we constructed a high order control volume discontinuous finite element method for both scalar and systems of hyperbolic conservation laws based on Lax–Wendroff time discretization. The method combines advantages of both control volume discontinuous finite element methods and Lax–Wendroff time discretization. The method can preserve local conservation. It is high order and high resolution. The limiter is only used once in each temporal discretization step. Several numerical examples are used to demonstrate the accuracy and high resolution of the method.