Convergence Of Time-Space Discontinuous Finite Elements For First Order Hyperbolic Systems

Ill this paper, a discontinuous finite element method for first order linear hyperbolic systems and semilinear hyperbolic systems is considered. The optimal order convergence on rectangular mesh is proved.Superconvergence at m + 1-order Radau points in each element is observed in our numerical experiments.To linear constant (variable) coefficient hyperbolic systems,equations whose slopes of characteristics are both positive or negative and those whose slopes of characteristic are either positive or negative are considered respectively. We solve the first type of hyperbolic systems in a cell by cell pat.ern and the second typo in a door by floor pa torn. We take the same scheme as C.Johnson used in 1986.Using tensor product analysis,we obtain the optimal order convergence theoretically.To similinear hyperbolic system, we use interpolated coefficient FEM and get similar results as the linear one.