EXPLICIT FINITE-ELEMENT METHODS FOR SCALAR HYPERBOLIC-EQUATIONS

We consider a class of finite element methods for scalar hyperbolic equations in which the approximate solution is developed "explicitly", one element at a time. Numerical results are presented for the discontinuous Galerkin method and several methods which yield a continuous approximation. Of the continuous methods tested, only one-that analyzed in [1]-shows optimal order accuracy. We present a new, simpler analysis for this method and establish a close relationship between it and the discontinuous Galerkin method.