THE OPTIMAL CONVERGENCE ORDER OF THE DISCONTINUOUS FINITE ELEMENT METHODS FOR FIRST ORDER HYPERBOLIC SYSTEMS

In this paper,a discontinuous finite element method for the positive and symmetric,first-order hyperbolic systems (steady and nonsteady state) is constructed and analyzedby using linear triangle elements,and the O(h~2)-order optimal error estimates are derivedunder the assumption of strongly regular triangulation and the H~3-regularity for the exactsolutions.The convergence analysis is based on some superclose estimates of the interpolationapproximation.Finally,we discuss the Maxwell equations in a two-dimensionaldomain,and numerical experiments are given to validate the theoretical results.