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