Title:         Analysis of a continuous finite element scheme for hyperbolic
               equations

Authors:       Richard S. Falk and Gerard R. Richter

Source:        SIAM J. NUMER.ANAL., vol. 24 (1987), pp. 257-278

Status:        Published

Abstract:      A finite element method for hyperbolic equations is analyzed in
               the context of a first order linear problem in R^2.  The method
               is applicable over a triangulation of the domain, and produces
               a continuous piecewise polynomial approximation, which can be
               developed in an explicit fashion from triangle to triangle.
               In a sense, it extends the basic upwind difference scheme to
               higher order.  The method is shown to be stable, and error
               estimates are obtained.  For nth degree approximation, the
               errors in the approximate solution and its gradient are shown
               to be at least of order h^{n+1/4} and h^{n-1/2}, respectively,
               assuming sufficient regularity in the solution.

Key words:     finite element method, hyperbolic equation

AMS(MOS) subject classifications. 65M15, 65N30