Abstract: Runge-Kutta control volume discontinuous finite element method (RKCVDFEM) is proposed to solve numerically hyperbolic conservation laws,in which space discretization is based on control volume finite element method (CVFEM) while time discretization is based on a second order accurate TVB Runge-Kutta technique.Piecewise linear function space is chosen as finite element space.The scheme is total variation bounded (TVB) and is formally second order accurate in space and time.Numerical examples show that numerical solution converges to the entropy solution,and order of convergence is optimal for smooth solution.Compared with numerical results of Runge-Kutta discontinuous Galerkin method (RKDGM) those of RKCVDFEM are better.

Key words: hyperbolic conservation laws, Runge-Kutta technique, control volume finite element method