Numerical Analysis Group
Research Report NA-95/24
Adaptive Lagrange-Galerkin methods for unsteady
convection-dominated diffusion problems
P Houston and
E Süli
1995, 57 pages.
In this paper we derive an a posteriori error estimate in the
L²(L²) norm for the Lagrange-Galerkin
discretisation of the unsteady two-dimensional convection-diffusion
problem. The proof of the error estimate is based on so-called strong
stability estimates of an associated backward dual problem, together
with the Galerkin orthogonality of the finite element method. Based on
this a posteriori error estimate, we design an adaptive
algorithm for determining both the space and time discretisation
parameters in such a way as to yield global error control in
the L²(L²) norm with respect to a
pre-determined tolerance. Moreover, the reliability and efficiency of
this adaptive strategy are numerically verified on test problems with
known analytic solutions.
- Key words and phrases:
- A posteriori error analysis, Lagrange-Galerkin finite
element methods, adaptive algorithms, reliability, efficiency
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 821,561 byte
gzipped PostScript file.
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