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