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

Abstract

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 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.