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Report no. 96/09

Finite element methods for hyperbolic

problems: a posteriori error analysis and

adaptivity a

Endre S?uli Paul Houston

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.

Subject classifications: AMS(MOS): 65M15, 65M50, 65M60

Key words and phrases: a posteriori error analysis, adaptivity, hyperbolic problems

The first author would like to acknowledge the financial support of the EPSRC.

The work reported here forms part of the research programme of the Oxford{Reading Institute for Computational Fluid Dynamics.

Oxford University Computing Laboratory
Numerical Analysis Group
Wolfson Building
Parks Road
Oxford, England OX1 3QD May, 1996

aPaper presented as Invited Lecture at the State of the Art in Numerical Analysis Conference, in York, 1-4 April 1996.