Title: Local error estimates for a finite element method for
hyperbolic and convection-diffusion equations
Authors: Richard S. Falk and Gerard R. Richter
Source: SIAM J. NUMER.ANAL., vol. 29 (1992), No. 3., pp. 730-754
Status: Published
Abstract: Local error estimates of near optimal order are derived for a finite
element method for hyperbolic and convection dominated
convection-diffusion equations in a domain $\Omega\subset R^2$.
The method generates, in an explicit fashion, a continuous piecewise
polynomial approximation of degree $n\geq 2$ over a triangulation of
$\Omega$. The scheme is shown to propagate disturbances a distance
$O(\sqrt{h} \log {1\over h})$ in the crosswind direction, where $h$
is the meshsize. The analysis uses test functions which depend only
on the crosswind variable. It is also shown to be applicable, in
a parallel fashion, to the discontinuous Galerkin method, thus
underscoring the close interrelationship of the two methods.
Key words: finite elements, hyperbolic equations, convection-diffusion
AMS(MOS) subject classifications. 65N30, 65M15