Numerical Analysis Group
Research Report NA-97/03
A Posteriori Error Analysis for Linear Convection-Diffusion
Problems Under Weak Mesh Regularity Assumptions
Paul Houston and
Endre Süli
May 1997, 31 pages.
In this paper we consider the generalisation of standard a
posteriori error estimates, derived for unsteady problems, to
arbitrary space-time meshes. In particular, we derive an a
posteriori error bound for the discontinuity capturing
Lagrange-Galerkin method applied to an unsteady (linear)
convection-diffusion problem, assuming only that the underlying mesh is
non-degenerate. The proof of this error estimate will be
based on strong stability estimates of an associated dual problem,
together with the Galerkin orthogonality of the finite element method.
- Key words and phrases:
- a posteriori error analysis,
quasi-interpolation operators,
Lagrange-Galerkin finite element methods
The work reported here forms part of the research programme of the
Oxford-Reading
Institute for Computational Fluid Dynamics.
This paper is available as a 145,026 byte
gzipped PostScript file.
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