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### 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 $H^{-1}$ 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.

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### Authors

Publisher:
Unspecified
Publication date:
1996-05-01
UUID:
uuid:1cc3f640-dac4-4a66-88ba-ea785a2196b3
Local pid:
oai:eprints.maths.ox.ac.uk:1324
Deposit date:
2011-06-12