Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity

Report

This paper presents an overview of recent developments in the area of a posteriori error estimation for first-order hyperbolic partial differential equations. Global a posteriori error bounds are derived in the $H^{-1}$ norm for steady and unsteady finite element and finite volume approximations of hyperbolic systems and scalar hyperbolic equations. We also consider the problem of a posteriori error estimation for linear functionals of the solution. The a posteriori error bounds are implemented into an adaptive finite element algorithm.

Authors: Suli, E; Houston, P

• Publisher: Unspecified
• Publication date: 1996-05-01