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Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems


Authors: Paul Houston and Endre Süli
Journal: Math. Comp. 70 (2001), 77-106
MSC (2000): Primary 65M15; Secondary 65M25, 65M60
DOI: https://doi.org/10.1090/S0025-5718-00-01187-X
Published electronically: March 3, 2000
MathSciNet review: 1681108
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Abstract:

In this paper we derive an a posteriori error bound for the Lagrange-Galerkin discretisation of an unsteady (linear) convection-diffusion problem, assuming only that the underlying space-time mesh is nondegenerate. The proof of this error bound is based on strong stability estimates of an associated dual problem, together with the Galerkin orthogonality of the finite element method. Based on this a posteriori bound, we design and implement the corresponding adaptive algorithm to ensure global control of the error with respect to a user-defined tolerance.


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Additional Information

Paul Houston
Affiliation: Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
Email: Paul.Houston@mcs.le.ac.uk

Endre Süli
Affiliation: Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
Email: Endre.Suli@comlab.ox.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-00-01187-X
Received by editor(s): December 16, 1997
Received by editor(s) in revised form: January 4, 1999
Published electronically: March 3, 2000
Additional Notes: We acknowledge the financial support of the EPSRC (Grant GR/K76221).
Article copyright: © Copyright 2000 American Mathematical Society