Numerical Analysis Group
Research Report NA-96/09
Finite element methods for hyperbolic problems:
a posteriori error analysis and adaptivity
Endre Süli and
Paul Houston
May 1996, 33 pages.
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 work reported here forms part of the research programme of the
Oxford-Reading
Institute for Computational Fluid Dynamics.
This paper was presented as Invited Lecture at the State of the Art
in Numerical Analysis Conference, in York, 1-4 April 1996.
It is available as a 465,982 byte
gzipped PostScript file.
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